From eac1c20b9d1bc4267e8abeb87043ad76e3e65b65 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Jean-S=C3=A9bastien?= Date: Tue, 8 Feb 2022 07:07:41 +0100 Subject: [PATCH] $msg --- build/a.html | 264 +----------------------- build/a_l.html | 264 +----------------------- build/c.html | 264 +----------------------- build/c_m.html | 264 +----------------------- build/c_m_cs.html | 264 +----------------------- build/c_m_cs_cyl.html | 290 ++------------------------- build/c_m_cs_hyp.html | 266 +----------------------- build/c_m_cs_sph.html | 287 ++------------------------ build/c_m_dc.html | 264 +----------------------- build/c_m_dc_curl.html | 264 +----------------------- build/c_m_dc_d2.html | 298 ++------------------------- build/c_m_dc_del.html | 264 +----------------------- build/c_m_dc_div.html | 264 +----------------------- build/c_m_dc_g.html | 264 +----------------------- build/c_m_dc_pr.html | 264 +----------------------- build/c_m_dd.html | 264 +----------------------- build/c_m_dd_1d.html | 264 +----------------------- build/c_m_dd_3d.html | 282 ++------------------------ build/c_m_dd_div.html | 264 +----------------------- build/c_m_ic.html | 266 +----------------------- build/c_m_ic_ftc.html | 266 +----------------------- build/c_m_ic_ftg.html | 264 +----------------------- build/c_m_ic_gauss.html | 264 +----------------------- build/c_m_ic_ip.html | 292 ++------------------------- build/c_m_ic_lsv.html | 286 ++------------------------ build/c_m_ic_stokes.html | 281 ++------------------------ build/c_m_uf.html | 266 +----------------------- build/c_m_uf_cyl.html | 264 +----------------------- build/c_m_uf_sph.html | 264 +----------------------- build/c_m_uf_vi.html | 264 +----------------------- build/c_m_va.html | 264 +----------------------- build/c_m_va_cp.html | 282 +------------------------- build/c_m_va_n.html | 264 +----------------------- build/c_m_va_pds.html | 264 +----------------------- build/c_m_va_sp.html | 264 +----------------------- build/c_m_va_tp.html | 264 +----------------------- build/c_m_vf.html | 264 +----------------------- build/c_m_vf_helm.html | 264 +----------------------- build/c_m_vf_pot.html | 268 +------------------------ build/d.html | 268 +------------------------ build/d_emd.html | 264 +----------------------- build/d_emd_ce.html | 264 +----------------------- build/d_emd_emw.html | 264 +----------------------- build/d_emf.html | 264 +----------------------- build/d_ems.html | 264 +----------------------- build/d_ems_ca.html | 264 +----------------------- build/d_ems_ms.html | 264 +----------------------- build/d_emsm.html | 264 +----------------------- build/d_emsm_msm.html | 264 +----------------------- build/d_m.html | 264 +----------------------- build/d_red.html | 264 +----------------------- build/emd.html | 272 +------------------------ build/emd_Fl.html | 264 +----------------------- build/emd_Fl_Fl.html | 272 +------------------------ build/emd_Fl_e.html | 268 +------------------------ build/emd_Fl_i.html | 270 +------------------------ build/emd_Fl_ief.html | 270 +------------------------ build/emd_Me.html | 264 +----------------------- build/emd_Me_Me.html | 270 +------------------------ build/emd_Me_dc.html | 268 +------------------------ build/emd_Me_ebM.html | 264 +----------------------- build/emd_Me_mc.html | 264 +----------------------- build/emd_ce.html | 272 +------------------------ build/emd_ce_amom.html | 266 +----------------------- build/emd_ce_ce.html | 266 +----------------------- build/emd_ce_mom.html | 268 +------------------------ build/emd_ce_mst.html | 274 +------------------------ build/emd_ce_poy.html | 282 ++------------------------ build/emd_emw.html | 272 +------------------------ build/emd_emw_ep.html | 268 +------------------------ build/emd_emw_mpw.html | 266 +----------------------- build/emd_emw_we.html | 266 +----------------------- build/emdm.html | 264 +----------------------- build/emdm_Me.html | 264 +----------------------- build/emdm_Me_Mem.html | 286 ++------------------------ build/emdm_Me_bc.html | 266 +----------------------- build/emdm_emwm.html | 264 +----------------------- build/emdm_emwm_ad.html | 264 +----------------------- build/emdm_emwm_ad_c.html | 264 +----------------------- build/emdm_emwm_plm.html | 266 +----------------------- build/emdm_emwm_refl.html | 264 +----------------------- build/emdm_emwm_refl_Ba.html | 264 +----------------------- build/emdm_emwm_refl_Fe.html | 264 +----------------------- build/emdm_emwm_refl_ni.html | 264 +----------------------- build/emdm_emwm_refl_oi.html | 272 +------------------------ build/emdm_emwm_refr.html | 264 +----------------------- build/emdm_emwm_wg.html | 264 +----------------------- build/emdm_emwm_wg_c.html | 264 +----------------------- build/emdm_emwm_wg_gw.html | 264 +----------------------- build/emdm_emwm_wg_r.html | 264 +----------------------- build/emf.html | 272 +------------------------ build/emf_g.html | 264 +----------------------- build/emf_g_Cg.html | 264 +----------------------- build/emf_g_Lg.html | 268 +------------------------ build/emf_svp.html | 276 +------------------------ build/ems.html | 264 +----------------------- build/ems_ca.html | 272 +------------------------ build/ems_ca_fe.html | 283 ++------------------------ build/ems_ca_fe_L.html | 270 +------------------------ build/ems_ca_fe_g.html | 270 +------------------------ build/ems_ca_fe_uP.html | 268 +------------------------ build/ems_ca_me.html | 264 +----------------------- build/ems_ca_me_Ed.html | 264 +----------------------- build/ems_ca_me_Eq.html | 264 +----------------------- build/ems_ca_me_a.html | 264 +----------------------- build/ems_ca_me_h.html | 272 +------------------------ build/ems_ca_me_md.html | 268 +------------------------ build/ems_ca_mi.html | 268 +------------------------ build/ems_ca_mi_fe.html | 264 +----------------------- build/ems_ca_mi_isc.html | 264 +----------------------- build/ems_ca_mi_o.html | 268 +------------------------ build/ems_ca_sv.html | 264 +----------------------- build/ems_ca_sv_car.html | 268 +------------------------ build/ems_ca_sv_cyl.html | 264 +----------------------- build/ems_ca_sv_sph.html | 272 +------------------------ build/ems_es.html | 282 ++------------------------ build/ems_es_c.html | 269 +------------------------ build/ems_es_c_cap.html | 266 +----------------------- build/ems_es_c_ic.html | 268 +------------------------ build/ems_es_c_p.html | 266 +----------------------- build/ems_es_c_sc.html | 264 +----------------------- build/ems_es_e.html | 272 +------------------------ build/ems_es_e_c.html | 266 +----------------------- build/ems_es_e_ccd.html | 270 +------------------------ build/ems_es_e_pcd.html | 266 +----------------------- build/ems_es_ec.html | 269 +------------------------ build/ems_es_ec_b.html | 268 +------------------------ build/ems_es_ec_c.html | 268 +------------------------ build/ems_es_ec_q.html | 268 +------------------------ build/ems_es_ec_s.html | 264 +----------------------- build/ems_es_ef.html | 271 +------------------------ build/ems_es_ef_Gl.html | 320 +++++------------------------ build/ems_es_ef_cE.html | 281 ++------------------------ build/ems_es_ef_ccd.html | 295 ++------------------------- build/ems_es_ef_pc.html | 312 ++++------------------------- build/ems_es_efo.html | 270 +------------------------ build/ems_es_efo_cl.html | 280 ++------------------------ build/ems_es_efo_e.html | 302 +++------------------------- build/ems_es_efo_exp.html | 285 ++------------------------ build/ems_es_efo_ps.html | 272 +------------------------ build/ems_es_ep.html | 273 +------------------------ build/ems_es_ep_PL.html | 270 +------------------------ build/ems_es_ep_bc.html | 266 +----------------------- build/ems_es_ep_c.html | 266 +----------------------- build/ems_es_ep_d.html | 278 +------------------------- build/ems_es_ep_ex.html | 290 +-------------------------- build/ems_es_ep_fp.html | 270 +------------------------ build/ems_ms.html | 272 +------------------------ build/ems_ms_BS.html | 264 +----------------------- build/ems_ms_BS_sc.html | 272 +------------------------ build/ems_ms_dcB.html | 264 +----------------------- build/ems_ms_dcB_BS.html | 278 +------------------------- build/ems_ms_dcB_sc.html | 266 +----------------------- build/ems_ms_lf.html | 264 +----------------------- build/ems_ms_lf_c.html | 268 +------------------------ build/ems_ms_lf_pc.html | 272 +------------------------ build/ems_ms_vp.html | 278 +------------------------- build/ems_ms_vp_LC.html | 266 +----------------------- build/ems_ms_vp_comp.html | 264 +----------------------- build/ems_ms_vp_mbc.html | 270 +------------------------ build/ems_ms_vp_me.html | 278 +------------------------- build/emsm.html | 272 +------------------------ build/emsm_esm.html | 264 +----------------------- build/emsm_esm_D.html | 274 +------------------------ build/emsm_esm_D_bc.html | 266 +----------------------- build/emsm_esm_d.html | 266 +----------------------- build/emsm_esm_di.html | 264 +----------------------- build/emsm_esm_di_ld.html | 288 ++------------------------ build/emsm_esm_fpo.html | 280 ++------------------------ build/emsm_esm_fpo_fid.html | 266 +----------------------- build/emsm_esm_fpo_pibc.html | 264 +----------------------- build/emsm_esm_p.html | 270 +------------------------ build/emsm_esm_s.html | 264 +----------------------- build/emsm_msm.html | 274 +------------------------ build/emsm_msm_H.html | 264 +----------------------- build/emsm_msm_H_A.html | 276 +------------------------ build/emsm_msm_a.html | 264 +----------------------- build/emsm_msm_fmo.html | 264 +----------------------- build/emsm_msm_fmo_bc.html | 286 ++------------------------ build/emsm_msm_fmo_fim.html | 264 +----------------------- build/emsm_msm_fmo_pibc.html | 264 +----------------------- build/emsm_msm_lnlm.html | 266 +----------------------- build/emsm_msm_lnlm_fm.html | 264 +----------------------- build/emsm_msm_lnlm_sp.html | 266 +----------------------- build/emsm_msm_m.html | 264 +----------------------- build/emsm_msm_m_dpf.html | 272 +------------------------ build/emsm_msm_m_fdi.html | 270 +------------------------ build/in.html | 264 +----------------------- build/in_p.html | 264 +----------------------- build/in_t.html | 264 +----------------------- build/in_t_c.html | 292 ++------------------------- build/index.html | 377 ++--------------------------------- build/qed.html | 264 +----------------------- build/qed_t.html | 264 +----------------------- build/red.html | 272 +------------------------ build/red_rem.html | 264 +----------------------- build/red_rem_Fmunu.html | 270 +------------------------ build/red_rem_Ltf.html | 266 +----------------------- build/red_rem_Me.html | 276 +------------------------ build/red_rem_mre.html | 266 +----------------------- build/red_rm.html | 264 +----------------------- build/red_rm_Mf.html | 270 +------------------------ build/red_rm_pt.html | 268 +------------------------ build/red_rm_rme.html | 272 +------------------------ build/red_sr.html | 264 +----------------------- build/red_sr_4v.html | 270 +------------------------ build/red_sr_Lt.html | 266 +----------------------- build/red_sr_p.html | 268 +------------------------ build/style.css | 20 +- 209 files changed, 1478 insertions(+), 54683 deletions(-) diff --git a/build/a.html b/build/a.html index 846583d..386f17d 100644 --- a/build/a.html +++ b/build/a.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Cylindrical Coordinates @@ -1928,14 +1672,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
    Gradient
    -
    +

    -
    +
    • Gr4(1.79)
    @@ -1962,14 +1706,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
    Divergence
    -
    +

    -
    +
    • Gr4(2.21)
    @@ -1980,10 +1724,10 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in

    \[ -{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r} \frac{\partial}{\partial r} (r vr) +{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r} \frac{\partial}{\partial r} (r v_r)

      -
    • \frac{1}{r} \frac{∂ vφ}{∂ φ} + \frac{\partial v_z}{\partial z}.
      • +
    • \frac{1}{r} \frac{∂ v_{φ}}{∂ φ} + \frac{\partial v_z}{\partial z}.

    \tag{cyl_div} @@ -1996,14 +1740,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in

    Curl
    -
    +

    -
    +
    • Gr4(2.21)
    @@ -2014,11 +1758,11 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in

    \[ -{\boldsymbol ∇} × {\bf v} = \left( \frac{1}{r} \frac{\partial v_z}{\partial \phi} - \frac{∂ vφ}{∂ z}\right) ~\hat{\bf r} +{\boldsymbol ∇} × {\bf v} = \left( \frac{1}{r} \frac{\partial v_z}{\partial \phi} - \frac{∂ v_{φ}}{∂ z}\right) ~\hat{\bf r}

    • \left( \frac{\partial v_r}{\partial z} - \frac{\partial v_z}{\partial r} \right) ~\hat{\boldsymbol \phi}
      • -
    • \frac{1}{r} \left( \frac{\partial}{\partial r} (r vφ) - \frac{\partial v_r}{\partial \phi} \right) ~\hat{\bf z}
      • +
    • \frac{1}{r} \left( \frac{\partial}{\partial r} (r v_{φ}) - \frac{\partial v_r}{\partial \phi} \right) ~\hat{\bf z}

    \tag{cyl_curl} @@ -2033,7 +1777,7 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in

    \[ -{\boldsymbol ∇}2 T = \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial T}{\partial r} \right) +{\boldsymbol ∇}^2 T = \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial T}{\partial r} \right)

    @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Hyperbolic Coordinates @@ -1880,7 +1624,7 @@ Table of contents
    diff --git a/build/c_m_cs_sph.html b/build/c_m_cs_sph.html index 551368b..c46a505 100644 --- a/build/c_m_cs_sph.html +++ b/build/c_m_cs_sph.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Spherical Coordinates c.m.cs.sph
    - -
    -sphere - -
    Figure 1: Sphere drawn with Asymptote
    -
    -

    \((r, \theta, \phi)\). \(\theta\) is the polar angle, \(\phi\) the azimuthal angle.

    @@ -1970,10 +1707,10 @@ Infinitesimal surface element: depends on situation.

    \[ -{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r^2} \frac{\partial}{\partial r} (r2 vr) + \frac{1}{r\sin \theta} \frac{\partial}{\partial \theta} (sinθ vθ) +{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 v_r) + \frac{1}{r\sin \theta} \frac{\partial}{\partial \theta} (sinθ v_{θ})

      -
    • \frac{1}{r \sin \theta} \frac{∂ vφ}{∂ φ}
      • +
    • \frac{1}{r \sin \theta} \frac{∂ v_{φ}}{∂ φ}

    \label{Gr(1.71)} @@ -1987,11 +1724,11 @@ Infinitesimal surface element: depends on situation.

    \[ -{\boldsymbol ∇} × {\bf v} = \frac{1}{r\sin \theta} \left[ \frac{\partial}{\partial \theta} (sin θ vφ) - \frac{∂ vθ}{∂ φ} \right] \hat{\bf r} +{\boldsymbol ∇} × {\bf v} = \frac{1}{r\sin \theta} \left[ \frac{\partial}{\partial \theta} (sin θ v_{φ}) - \frac{∂ v_{θ}}{∂ φ} \right] \hat{\bf r}

      -
    • \frac{1}{r} \left[ \frac{1}{\sin \theta} \frac{\partial v_r}{\partial \phi} - \frac{\partial}{\partial r} (r vφ) \right] \hat{\boldsymbol \theta}
      • -
    • \frac{1}{r} \left[ \frac{\partial}{\partial r} (r vθ) - \frac{\partial v_r}{\partial \theta} \right] \hat{\boldsymbol \phi}
      • +
    • \frac{1}{r} \left[ \frac{1}{\sin \theta} \frac{\partial v_r}{\partial \phi} - \frac{\partial}{\partial r} (r v_{φ}) \right] \hat{\boldsymbol \theta}
      • +
    • \frac{1}{r} \left[ \frac{\partial}{\partial r} (r v_{θ}) - \frac{\partial v_r}{\partial \theta} \right] \hat{\boldsymbol \phi}

    \label{Gr(1.72)} @@ -2005,7 +1742,7 @@ Infinitesimal surface element: depends on situation.

    \[ -{\boldsymbol ∇}2 T = \frac{1}{r^2} \frac{\partial}{\partial r} \left(r2 \frac{\partial T}{\partial r}\right) +{\boldsymbol ∇}^2 T = \frac{1}{r^2} \frac{\partial}{\partial r} \left(r^2 \frac{\partial T}{\partial r}\right)

    @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Second Derivatives @@ -1876,9 +1620,9 @@ Table of contents
    -
    -
    Divergence of gradient
    -
    +
    +
    Divergence of gradient
    +

    \({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) is called the Laplacian of the scalar field \(T\). The Laplacian of a vector field \({\boldsymbol \nabla}^2 {\bf v}\) is also defined as the vector with components @@ -1887,36 +1631,36 @@ given by the Laplacian of the corresponding vector elements.

    -
    -
    Curl of a gradient
    -
    +
    +
    Curl of a gradient
    +

    This always vanishes.

    -
    -
    Gradient of the divergence
    -
    +
    +
    Gradient of the divergence
    +

    \({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name.

    -
    -
    Divergence of a curl
    -
    +
    +
    Divergence of a curl
    +

    This always vanishes.

    -
    -
    Curl of curl
    -
    +
    +
    Curl of curl
    +

    \[ {\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v} @@ -1930,7 +1674,7 @@ This always vanishes.

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/c_m_dc_del.html b/build/c_m_dc_del.html index 0077ff0..646c045 100644 --- a/build/c_m_dc_del.html +++ b/build/c_m_dc_del.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    - +

    Integral Calculus @@ -1890,7 +1634,7 @@ Table of contents
    diff --git a/build/c_m_ic_ftc.html b/build/c_m_ic_ftc.html index 5c28d48..6fe777d 100644 --- a/build/c_m_ic_ftc.html +++ b/build/c_m_ic_ftc.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    The Fundamental Theorem of Calculus @@ -1888,7 +1632,7 @@ Table of contents
    diff --git a/build/c_m_ic_ftg.html b/build/c_m_ic_ftg.html index d8cfae7..3a0456a 100644 --- a/build/c_m_ic_ftg.html +++ b/build/c_m_ic_ftg.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/c_m_ic_lsv.html b/build/c_m_ic_lsv.html index 423075e..fde2ff3 100644 --- a/build/c_m_ic_lsv.html +++ b/build/c_m_ic_lsv.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Line, Surface and Volume Integrals @@ -1876,9 +1620,9 @@ Table of contents
    -
    -
    Line Integrals
    -
    +
    +
    Line Integrals
    +

    \[ {\int_{\bf a}^{\bf b}}_{\cal P} {\bf v} \cdot d{\bf l} @@ -1907,9 +1651,9 @@ Integral over a closed loop:

    -
    -
    Surface Integrals
    -
    +
    +
    Surface Integrals
    +

    \[ \int_{\cal S} {\bf v} \cdot d{\bf a} @@ -1929,9 +1673,9 @@ Over a closed surface:

    -
    -
    Volume Integrals
    -
    +
    +
    Volume Integrals
    +

    \[ \int_{\cal V} T d\tau @@ -1959,7 +1703,7 @@ d\tau = dx dy dz

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/c_m_ic_stokes.html b/build/c_m_ic_stokes.html index dc50a34..be76a7a 100644 --- a/build/c_m_ic_stokes.html +++ b/build/c_m_ic_stokes.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    +
    +

    + + + + +

    +
    +
      +
    • Gr (1.57)
      • +
    + +
    + +

    \[ \int_{\cal S} ({\boldsymbol \nabla} \times {\bf v}) \cdot d{\bf a} = \oint_{\cal P} {\bf v} \cdot d{\bf l}. -\label{Gr(1.57)} +\tag{Stokes}\label{Stokes} \]

    @@ -1898,7 +1657,7 @@ the boundary shrinks to a point.

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/c_m_uf.html b/build/c_m_uf.html index dc258cb..879c3a6 100644 --- a/build/c_m_uf.html +++ b/build/c_m_uf.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    - +

    Useful Formulas @@ -1887,7 +1631,7 @@ Table of contents
    diff --git a/build/c_m_uf_cyl.html b/build/c_m_uf_cyl.html index c90f4fe..6626a83 100644 --- a/build/c_m_uf_cyl.html +++ b/build/c_m_uf_cyl.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents

    -

    -\[ - {\bf A} × {\bf B} = \left| \begin{array}{ccc} \hat{x} & \hat{y} & \hat{z}
    - Ax & Ay & Az \\ Bx & By & Bz \end{array} \right| - = \left( Ay Bz - Az By \right) \hat{x} + \left( Bz Ax - Bx Az \right) \hat{y} -

    -
      -
    • \left( Ax By - Ay Bx \right) \hat{z}
      • -
    -

    -\] -

    +\begin{equation*} + {\bf A} \times {\bf B} = \left| \begin{array}{ccc} \hat{x} & \hat{y} & \hat{z} \\ + A_x & A_y & A_z \\ B_x & B_y & B_z \end{array} \right| + = \left( A_y B_z - A_z B_y \right) \hat{x} + \left( B_z A_x - B_x A_z \right) \hat{y} + + \left( A_x B_y - A_y B_x \right) \hat{z} +\end{equation*}

    The cross product is distributive: @@ -1924,7 +1662,7 @@ this relation making plain that

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/c_m_va_n.html b/build/c_m_va_n.html index 1f90070..b7121f6 100644 --- a/build/c_m_va_n.html +++ b/build/c_m_va_n.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Potentials @@ -1934,7 +1678,7 @@ The following conditions are equivalent:
    diff --git a/build/d.html b/build/d.html index c6f5567..05262db 100644 --- a/build/d.html +++ b/build/d.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    - +
    + Objectives @@ -1927,7 +1671,7 @@ I have little doubt you'll pass the course.

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/d_emd.html b/build/d_emd.html index 59476a9..1b899c8 100644 --- a/build/d_emd.html +++ b/build/d_emd.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents

    -
    - +
    + Prerequisites
      @@ -1885,8 +1629,8 @@ Prerequisites
    -
    - +
    + Objectives @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    @@ -926,21 +817,8 @@ Table of contents @@ -1645,29 +1477,8 @@ Table of contents @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    - +
    + Prerequisites
      @@ -1884,8 +1628,8 @@ Prerequisites
    -
    - +
    + Objectives @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    @@ -926,21 +817,8 @@ Table of contents @@ -1645,29 +1477,8 @@ Table of contents @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    - +
    + Prerequisites
      @@ -1885,8 +1629,8 @@ Prerequisites
    -
    - +
    + Objectives @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    @@ -926,21 +817,8 @@ Table of contents @@ -1645,29 +1477,8 @@ Table of contents @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    - +
    + Prerequisites
      @@ -1884,8 +1628,8 @@ Prerequisites
    -
    - +
    + Objectives @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    @@ -926,21 +817,8 @@ Table of contents @@ -1645,29 +1477,8 @@ Table of contents @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Green's Identities ems.ca.fe.g
    -
    +

    George Green

    -
    +

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/ems_es_ec_s.html b/build/ems_es_ec_s.html index 1f444b4..5ebd06d 100644 --- a/build/ems_es_ec_s.html +++ b/build/ems_es_ec_s.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    - +

    Electrostatic Fields ems.es.ef

    +
      +
    • FLS II 1,4
      • +
    • Gr 2.1-2
      • +
    • PM 1.7-13
      • +
    @@ -1888,7 +1637,7 @@ Table of contents

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/ems_es_ef_Gl.html b/build/ems_es_ef_Gl.html index 764a256..794ed27 100644 --- a/build/ems_es_ef_Gl.html +++ b/build/ems_es_ef_Gl.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -426,26 +380,9 @@ Table of contents The Curl of \({\bf E}\)ems.es.ef.cE -
  • - -
    - +
  • Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - -
    •  - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Gauss's Law: the divergence of \({\bf E}\) @@ -1911,7 +1655,7 @@ sphere of radius \(r\) around the charge,

    \[ \oint {\bf E} \cdot d{\bf a} = \frac{1}{4\pi\varepsilon_0} \int_{\cal S} \frac{q}{r^2} \hat{\bf r} \cdot \hat{\bf r} -r^2 \sin \theta d\theta d\phi = \frac{q}{\varepsilon_0} +~r^2 \sin \theta d\theta d\phi = \frac{q}{\varepsilon_0} \label{Gr(2.12)} \]

    @@ -1919,7 +1663,22 @@ r^2 \sin \theta d\theta d\phi = \frac{q}{\varepsilon_0}

    so by superposition, we obtain

    -
    +
    +

    + + + + +

    +
    +
      +
    • Gr (2.13)
      • +
    + +
    + +
    +

    Gauss' law (in integral form)

    @@ -1927,7 +1686,7 @@ so by superposition, we obtain

    \[ \oint_{\cal S} {\bf E} \cdot d{\bf a} = \frac{Q_{\mbox{enc}}}{\varepsilon_0} - \label{Gr(2.13)} + \tag{Gl_i}\label{Gl_i} \]

    @@ -1951,7 +1710,22 @@ By applying the divergence theorem, and using \(Q_{\mbox{enc}} = \int_{\cal V} \rho d\tau\), and using the fact the the choice of volume is arbitrary, we get

    -
    +
    +

    + + + + +

    +
    +
      +
    • Gr (2.14)
      • +
    + +
    + +
    +

    Gauss' law in differential form

    @@ -1959,14 +1733,14 @@ is arbitrary, we get

    \[ {\boldsymbol \nabla} \cdot {\bf E} = \frac{\rho}{\varepsilon_0}. - \label{Gr(2.14)} + \tag{Gl_d}\label{Gl_d} \]

    -We can also compute the divergence of \({\bf E}\) directly from \ref{eq:E_from_rho}: +We can also compute the divergence of \({\bf E}\) directly from E_vcd:

    @@ -1976,7 +1750,7 @@ We can also compute the divergence of \({\bf E}\) directly from \ref{eq:E_from_r

    -Using \ref{Gr(1.100)}, +Using divdel,

    @@ -2010,7 +1784,7 @@ cylindrical or plane symmetry. Gaussian surfaces: respectively, concentric sphere, coaxial cylinder, pillbox.

    -
    +

    Example 2.2: Field outside a uniformly charged sphere of radius \(R\) and total charge \(q\).

    @@ -2041,7 +1815,7 @@ Same as point charge at origin!
    -
    +

    Example 2.3: infinitely long cylinder carrying charge density \(\rho = k s\) for some constant \(k\). Find \({\bf E}\) within the cylinder.

    @@ -2080,7 +1854,7 @@ Therefore,
    -
    +

    Example 2.4: infinite plane (defined by \(z = 0\)) with uniform surface charge density \(\sigma\). Find \({\bf E}\).

    @@ -2106,7 +1880,7 @@ where \(\hat{\bf n}\) is a unit vector extending away from the plane. Independe
    -
    +

    Example 2.5: two infinite planes (put them vertical) carrying equal but opposite uniform surface charge densities \(\pm \sigma\).

    @@ -2123,7 +1897,7 @@ where \(\hat{\bf n}\) is a unit vector extending away from the plane. Independe

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/ems_es_ef_cE.html b/build/ems_es_ef_cE.html index e4e2e12..bd1b924 100644 --- a/build/ems_es_ef_cE.html +++ b/build/ems_es_ef_cE.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents

    -As a consequence of \ref{Gr(2.22)}, we immediately see that the work done when travelling -in any closed path vanishes, that is: +Since the work done when moving on a closed path vanishes, we have

    -
    +

    -
    +
    • Gr (2.19)
    @@ -1894,7 +1637,7 @@ in any closed path vanishes, that is:
    -
    +

    @@ -1909,17 +1652,17 @@ in any closed path vanishes, that is:

    -which by Stokes' theorem implies that the electrostatic field is curlless, +which by Stokes' theorem implies that the electrostatic field is curlless,

    -
    +

    -
    +
    • Gr (2.20)
    @@ -1927,7 +1670,7 @@ which by Stokes' theorem implies that the electrostatic field is curlless,
    -
    +

    \[ {\boldsymbol \nabla} \times {\bf E} = 0. @@ -1956,7 +1699,7 @@ falls off, has the property that the work done is independent of the path.

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/ems_es_ef_ccd.html b/build/ems_es_ef_ccd.html index 5d18599..cb193e0 100644 --- a/build/ems_es_ef_ccd.html +++ b/build/ems_es_ef_ccd.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Experimental Investigations ems.es.efo.exp
    -
    -
    Before Coulomb
    + + -
    -
    Cavendish's experiment
    + -
    -
    Coulomb
    + - @@ -1894,7 +1639,7 @@ Table of contents

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/ems_es_efo_ps.html b/build/ems_es_efo_ps.html index 13d3e1a..1fc23fb 100644 --- a/build/ems_es_efo_ps.html +++ b/build/ems_es_efo_ps.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    - -

    Electrostatic Potential + +

    The Electrostatic Potential ems.es.ep

    +
      +
    • FLS II 4-3–4
      • +
    • Gr 2.3
      • +
    • PM 2
      • +
    @@ -1890,7 +1639,7 @@ Table of contents

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/ems_es_ep_PL.html b/build/ems_es_ep_PL.html index 6e7ed7d..9e7c09b 100644 --- a/build/ems_es_ep_PL.html +++ b/build/ems_es_ep_PL.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    The Poisson Equation and the Laplace Equation @@ -1883,7 +1627,7 @@ Our two fundamental equations for the electrostatic field are \] For the electrostatic potential, Gauss' law becomes

    -
    +

    The Poisson equation \[ @@ -1896,7 +1640,7 @@ For the electrostatic potential, Gauss' law becomes

    When the charge density vanishes, it becomes more simply

    -
    +

    The Laplace Equation \[ @@ -1919,7 +1663,7 @@ Since the curl of a gradient is always zero, we by construction have

    diff --git a/build/ems_es_ep_bc.html b/build/ems_es_ep_bc.html index 61f77a2..b14740e 100644 --- a/build/ems_es_ep_bc.html +++ b/build/ems_es_ep_bc.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Electrostatic Boundary Conditions @@ -1948,7 +1692,7 @@ if the surface charge is known.
    diff --git a/build/ems_es_ep_c.html b/build/ems_es_ep_c.html index 516388d..d9cf179 100644 --- a/build/ems_es_ep_c.html +++ b/build/ems_es_ep_c.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Comments on the Electrostatic Potential @@ -1902,7 +1646,7 @@ In the SI system where the ampere is a base unit, a volt is a \(kg m^2/s^3 A\).
    diff --git a/build/ems_es_ep_d.html b/build/ems_es_ep_d.html index 55edeb9..720137e 100644 --- a/build/ems_es_ep_d.html +++ b/build/ems_es_ep_d.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Definition @@ -1877,14 +1621,14 @@ Table of contents

    Since this work is independent of the path chosen, we can define a function called the electrostatic potential

    -
    +

    -
    +
    • Gr (2.21)
    @@ -1900,7 +1644,7 @@ V({\bf r}) \equiv -\int_{\cal O}^{\bf r} {\bf E} \cdot d{\bf l} where \({\cal O}\) is some chosen reference point. The potential difference between two points is well-defined without the need to specify the reference point,

    -
    +

    \[ V({\bf b}) - V({\bf a}) = - \int_{\bf a}^{\bf b} {\bf E} \cdot d{\bf l} @@ -1922,7 +1666,7 @@ V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \frac{q}{r} The electrostatic potential moreover inherits the superposition principle from the electric field, so for a distribution of point charges \(q_i\) at positions \({\bf r}_i\), we have

    -
    +

    \[ V({\bf r}) = \frac{1}{4\pi\varepsilon_0} \sum_{i} \frac{q_i}{|{\bf r} - {\bf r}_i|} @@ -1934,7 +1678,7 @@ so for a distribution of point charges \(q_i\) at positions \({\bf r}_i\), we ha

    For a continuous charge density in a volume \({\cal V}\), we have

    -
    +

    \[ V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\cal V} d\tau' \frac{\rho({\bf r}')}{|{\bf r} - {\bf r}'|}, @@ -1946,7 +1690,7 @@ For a continuous charge density in a volume \({\cal V}\), we have

    whereas for a surface or line charge distribution, respectively,

    -
    +

    \[ V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\cal S} da' \frac{\sigma({\bf r}')}{|{\bf r} - {\bf r}'|}, @@ -1964,7 +1708,7 @@ whereas for a surface or line charge distribution, respectively,

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/ems_es_ep_ex.html b/build/ems_es_ep_ex.html index cbe1088..cf8c2af 100644 --- a/build/ems_es_ep_ex.html +++ b/build/ems_es_ep_ex.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Example calculations for the potential ems.es.ep.ex
    -
    +

    Example 2.6: find the potential inside and outside a spherical shell or radius \(R\) centered at origin, which carries uniform surface charge. Ref point at infinity. @@ -1896,7 +1640,7 @@ V(r < R) = V(R) = \frac{1}{4\pi \varepsilon_0} \frac{q}{R}.

    -
    +

    Example 2.7: find the potential of a uniformly charged spherical shell of radius \(R\) (same problem as 2.6, but now done with \ref{Gr(2.30)}). Solution: Use @@ -1904,25 +1648,11 @@ V(r < R) = V(R) = \frac{1}{4\pi \varepsilon_0} \frac{q}{R}. V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int da' \frac{\sigma}{|{\bf r} - {\bf r}'|}. \] Put \({\bf r}\) on \(\hat{\bf z}\) axis so \({\bf r} = z \hat{\bf z}\), use law of cosines: -\[

    - - - --- -- - - - - - - -
    {\bf r} - {\bf r}'= R2 + z2 - 2Rz cos θ'
    +\begin{equation} +|{\bf r} - {\bf r}'| = R^2 + z^2 - 2Rz \cos \theta' +\end{equation}

    -\] Element of surface area: \(R^2 \sin \theta' d\theta' d\phi'\), so

    \begin{align} @@ -1953,7 +1683,7 @@ and \(V(z) = \frac{1}{4\pi \varepsilon_0} \frac{q}{R}\) inside.

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/ems_es_ep_fp.html b/build/ems_es_ep_fp.html index 85542b7..e98b3b7 100644 --- a/build/ems_es_ep_fp.html +++ b/build/ems_es_ep_fp.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Field in terms of the potential ems.es.ep.fp

    -Relation espot gives us the potential in terms of the field. Let us now try to find +Relation es_pot gives us the potential in terms of the field. Let us now try to find a relationship giving the field in terms of the potential. For this, we look again at \ref{Gr(2.22)}. By the fundamental theorm for gradients, this also equals \[ @@ -1887,7 +1631,7 @@ so \] Since this is true for any choice of \({\bf a}\) and \({\bf b}\), we have

    -
    +

    \[ {\bf E} = -{\boldsymbol \nabla} V @@ -1914,7 +1658,7 @@ by using \ref{Gr(1.101)} and \ref{Gr(2.27)}.

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/ems_ms.html b/build/ems_ms.html index 5025b27..b882940 100644 --- a/build/ems_ms.html +++ b/build/ems_ms.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    - +
    + Prerequisites
      @@ -1884,8 +1628,8 @@ Prerequisites
    -
    - +
    + Objectives @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    @@ -926,21 +817,8 @@ Table of contents @@ -1645,29 +1477,8 @@ Table of contents @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    - +
    + Prerequisites
      @@ -1885,8 +1629,8 @@ Prerequisites
    -
    - +
    + Objectives @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    @@ -926,21 +817,8 @@ Table of contents @@ -1645,29 +1477,8 @@ Table of contents @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Linear Dielectrics @@ -1882,7 +1626,7 @@ Table of contents

    For many substances: polarization is proportional to field, if the latter isn't too strong:

    -
    +

    \[ {\bf P} = \varepsilon_0 \chi_e {\bf E} @@ -1912,7 +1656,7 @@ In linear dielectrics: \] so

    -
    +

    \[ {\bf D} = \varepsilon {\bf E} @@ -1934,7 +1678,7 @@ This is all just nomenclature, everything is already in \ref{Gr(4.30)}. -

    +

    \paragraph{Example 4.5:} metal sphere of radius \(a\) carrying charge \(Q\), surrounded out to radius \(b\) by a linear dielectric material of permittivity \(\varepsilon\). Find potential at center (relative to infinity). @@ -1990,7 +1734,7 @@ of {\it e.g.} \({\bf P}\) would not vanish. Only case where parallel works: space entirely filled with homogeneous linear dielectric.

    -
    +

    \paragraph{Example 4.6:} parallel-plate capacitor filled with insulating material of dielectric constant \(\varepsilon_r\). What is the effect on the capacitance ? @@ -2025,7 +1769,7 @@ If \(\rho = 0\), any net charge is on surface, potential then obeys Laplace.

    Convenient to rewrite boundary conditions in terms of free charge: from \ref{Gr(4.26)},

    -
    +

    \[ \varepsilon_{above} E^{\perp}_{above} - \varepsilon_{below} E^{\perp}_{below} = \sigma_f @@ -2037,7 +1781,7 @@ Convenient to rewrite boundary conditions in terms of free charge: from \ref{Gr

    or in terms of the potential,

    -
    +

    \[ \varepsilon_{above} \frac{\partial V_{above}}{\partial n} - @@ -2050,7 +1794,7 @@ or in terms of the potential,

    Potential itself is continuous,

    -
    +

    \[ V_{above} = V_{below} @@ -2062,7 +1806,7 @@ Potential itself is continuous, -

    +

    \paragraph{Example 4.7:} sphere of homogeneous dielectric material in uniform electric field \({\bf E}_0\). Find electric field inside sphere. @@ -2120,7 +1864,7 @@ Thus, -

    +

    \paragraph{Example 4.8:} suppose region below \(z = 0\) is filled with uniform linear dielectric with susceptibility \(\chi_e\). Calculate force on point charge \(q\) situated a distance \(d\) above origin. @@ -2224,7 +1968,7 @@ Special case of linear isotropic dielectric: \({\bf D} = \varepsilon {\bf E}\), \] Total work done:

    -
    +

    \[ W = \frac{1}{2} \int d\tau {\bf D} \cdot {\bf E} @@ -2315,7 +2059,7 @@ so like before but with the correct sign.

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/emsm_esm_fpo.html b/build/emsm_esm_fpo.html index aab5aad..f129140 100644 --- a/build/emsm_esm_fpo.html +++ b/build/emsm_esm_fpo.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    - +

    Magnetostatics in matter emsm.msm

    -
    - +
    + Prerequisites
      @@ -1885,8 +1629,8 @@ Prerequisites
    -
    - +
    + Objectives @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    @@ -926,21 +817,8 @@ Table of contents @@ -1645,29 +1477,8 @@ Table of contents @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Ampère's Law in Magnetized Materials @@ -1888,7 +1632,7 @@ Ampère's law: \] so we can define

    -
    +

    \[ {\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M} @@ -1900,7 +1644,7 @@ so we can define

    and rewrite Ampère's law as

    -
    +

    \[ {\boldsymbol \nabla} \times {\bf H} = {\bf J}_f @@ -1912,7 +1656,7 @@ and rewrite Ampère's law as

    or in integral form,

    -
    +

    \[ \oint {\bf H} \cdot d{\bf l} = I_{f_{enc}} @@ -1926,7 +1670,7 @@ or in integral form, rewrite Ampère's law in terms of free currents alone. Bound currents come along for the ride.

    -
    +

    \paragraph{Example 6.2:} long copper rod radius \({\bf R}\) carries uniformly distributed free current \(I\). Find \({\bf H}\) inside and outside rod. @@ -2032,7 +1776,7 @@ and

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/emsm_msm_a.html b/build/emsm_msm_a.html index ff240db..9366379 100644 --- a/build/emsm_msm_a.html +++ b/build/emsm_msm_a.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    - +

    Linear and Nonlinear Media @@ -1886,7 +1630,7 @@ Table of contents
    diff --git a/build/emsm_msm_lnlm_fm.html b/build/emsm_msm_lnlm_fm.html index 51fd9c9..40e2fca 100644 --- a/build/emsm_msm_lnlm_fm.html +++ b/build/emsm_msm_lnlm_fm.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Diamagnetism, Paramagnetism, Ferromagnetism @@ -1885,8 +1629,8 @@ Table of contents

    - @@ -1897,7 +1641,7 @@ Table of contents

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/emsm_msm_m_fdi.html b/build/emsm_msm_m_fdi.html index 1616922..03dc47e 100644 --- a/build/emsm_msm_m_fdi.html +++ b/build/emsm_msm_m_fdi.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    +
    Torques and Forces on Magnetic Dipoles @@ -1877,7 +1621,7 @@ Table of contents

    Torque on magnetic dipole:

    -
    +

    \[ {\bf N} = {\bf m} \times {\bf B} @@ -1895,7 +1639,7 @@ Similar to electric analogue, \ref{Gr(4.4)}, \({\bf N} = {\bf p} \times {\bf E}\

    In a non-uniform field: (to be done in Problem 6.4):

    -
    +

    \[ {\bf F} = {\boldsymbol \nabla} ({\bf m} \cdot {\bf B}) @@ -1911,7 +1655,7 @@ In a non-uniform field: (to be done in Problem 6.4):

    diff --git a/build/in.html b/build/in.html index 31a5a1e..6fb703c 100644 --- a/build/in.html +++ b/build/in.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    - +
    + Objectives

    @@ -1907,8 +1651,8 @@ Objectives for this part: what you should learn by reading this

    -
    - +
    + Core

    @@ -1916,8 +1660,8 @@ Core material: you have to know this by heart, and how to use it.

    -
    - +
    + Main

    @@ -1925,8 +1669,8 @@ Main matter which you should know how to use.

    -
    - +
    + Example

    @@ -1934,8 +1678,8 @@ Example of the concepts just covered.

    -
    - +
    + Info

    @@ -1943,8 +1687,8 @@ Additional (contextual) information.

    -
    - +
    + Historical Context

    @@ -1957,7 +1701,7 @@ Additional historical context.

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/index.html b/build/index.html index bcd1e87..7d0cc0e 100644 --- a/build/index.html +++ b/build/index.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
  • - -
    - Experimental Investigationsems.es.efo.exp - - - -
    -
    • -
  • - -
    - Energy in Systems of Point Chargesems.es.efo.e - - - -
    • @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    @@ -926,21 +817,8 @@ Table of contents
    @@ -1599,37 +1460,8 @@ Table of contents
  • - -
    - Second Derivativesc.m.dc.d2 - - - -
    • @@ -1645,29 +1477,8 @@ Table of contents
    @@ -1909,23 +1653,8 @@ Table of contents
  • @@ -1934,17 +1663,11 @@ Table of contents
  • Electrostatic Field of Point Chargesems.es.ef.pc
  • Electrostatic Field of Continuous Charge Distributionsems.es.ef.ccd
  • The Curl of \({\bf E}\)ems.es.ef.cE
    • -
  • -Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - -
    • +
  • Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl
  • -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep
  • -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -2099,12 +1807,7 @@ Table of contents
  • Magnetizationemsm.msm.m @@ -2120,13 +1823,7 @@ Table of contents
  • The H Fieldemsm.msm.H
  • @@ -2318,29 +2015,13 @@ Table of contents
  • The Divergencec.m.dc.div
  • The Curlc.m.dc.curl
  • Product Rulesc.m.dc.pr
    • -
  • -Second Derivativesc.m.dc.d2 - -
    • +
  • Second Derivativesc.m.dc.d2
  • Integral Calculusc.m.ic @@ -427,25 +381,8 @@ Table of contents
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    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    -
    - +
    + Prerequisites
      @@ -1884,8 +1628,8 @@ Prerequisites
    -
    - +
    + Objectives @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents
    @@ -926,21 +817,8 @@ Table of contents @@ -1645,29 +1477,8 @@ Table of contents @@ -427,25 +381,8 @@ Table of contents
  • - -
    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
    • @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
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    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents

    -
    +

    The {\bf relativistic momentum} \({\boldsymbol p}\) is defined as \[ @@ -1896,7 +1640,7 @@ These can be combined into the {\bf energy-momentum four-vector}

    When the object is stationary, its energy is the

    -
    +

    {\bf Rest energy} \[ @@ -1909,7 +1653,7 @@ When the object is stationary, its energy is the When moving, the difference between relativistic and rest energies is the

    -
    +

    {\bf Kinetic energy} \[ @@ -1929,7 +1673,7 @@ this to

    In a closed system,

    -
    +

    {\bf Total relativistic energy and momentum is conserved} \[ @@ -1950,7 +1694,7 @@ N.B.: don't confuse an {\bf invariant} quantity with a {\bf conserved} quantity.

    Author: Jean-Sébastien Caux

    -

    Created: 2022-02-07 Mon 08:02

    +

    Created: 2022-02-08 Tue 06:55

    Validate

    diff --git a/build/red_sr.html b/build/red_sr.html index 01a351a..e3b278c 100644 --- a/build/red_sr.html +++ b/build/red_sr.html @@ -1,7 +1,7 @@ - + Pre-Quantum Electrodynamics @@ -348,58 +348,12 @@ Table of contents
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    - Experimental Investigationsems.es.efo.exp - - - -
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    - Energy in Systems of Point Chargesems.es.efo.e - - - -
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    - Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl - - - -
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    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents @@ -455,7 +392,7 @@ Table of contents
    -Electrostatic Potentialems.es.ep +The Electrostatic Potentialems.es.ep @@ -492,7 +429,7 @@ Table of contents
    -Electrostatic Energyems.es.e +Electrostatic Energy from the Potentialems.es.e @@ -565,29 +502,8 @@ Table of contents