From 3454aba504af8e23a9021cda963fa1f822436e6f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jean-S=C3=A9bastien?=
Date: Tue, 8 Feb 2022 17:21:33 +0100
Subject: [PATCH] Update 2022-02-08 17:21
---
build/a.html | 10 +++-
build/a_l.html | 10 +++-
build/c.html | 10 +++-
build/c_m.html | 10 +++-
build/c_m_cs.html | 10 +++-
build/c_m_cs_cyl.html | 106 +++++++++++++----------------------
build/c_m_cs_hyp.html | 10 +++-
build/c_m_cs_sph.html | 70 +++++++++--------------
build/c_m_dc.html | 10 +++-
build/c_m_dc_curl.html | 10 +++-
build/c_m_dc_d2.html | 40 +++++++------
build/c_m_dc_del.html | 10 +++-
build/c_m_dc_div.html | 10 +++-
build/c_m_dc_g.html | 10 +++-
build/c_m_dc_pr.html | 10 +++-
build/c_m_dd.html | 10 +++-
build/c_m_dd_1d.html | 10 +++-
build/c_m_dd_3d.html | 50 +++++++----------
build/c_m_dd_div.html | 24 ++++----
build/c_m_ic.html | 10 +++-
build/c_m_ic_ftc.html | 10 +++-
build/c_m_ic_ftg.html | 10 +++-
build/c_m_ic_gauss.html | 10 +++-
build/c_m_ic_ip.html | 10 +++-
build/c_m_ic_lsv.html | 28 +++++----
build/c_m_ic_stokes.html | 14 +++--
build/c_m_uf.html | 10 +++-
build/c_m_uf_cyl.html | 10 +++-
build/c_m_uf_sph.html | 10 +++-
build/c_m_uf_vi.html | 10 +++-
build/c_m_va.html | 10 +++-
build/c_m_va_cp.html | 10 +++-
build/c_m_va_n.html | 10 +++-
build/c_m_va_pds.html | 10 +++-
build/c_m_va_sp.html | 10 +++-
build/c_m_va_tp.html | 10 +++-
build/c_m_vf.html | 10 +++-
build/c_m_vf_helm.html | 10 +++-
build/c_m_vf_pot.html | 16 +++---
build/d.html | 14 +++--
build/d_emd.html | 10 +++-
build/d_emd_ce.html | 10 +++-
build/d_emd_emw.html | 10 +++-
build/d_emf.html | 10 +++-
build/d_ems.html | 10 +++-
build/d_ems_ca.html | 10 +++-
build/d_ems_ms.html | 10 +++-
build/d_emsm.html | 10 +++-
build/d_emsm_msm.html | 10 +++-
build/d_m.html | 10 +++-
build/d_red.html | 10 +++-
build/emd.html | 18 +++---
build/emd_Fl.html | 10 +++-
build/emd_Fl_Fl.html | 16 ++++--
build/emd_Fl_e.html | 14 +++--
build/emd_Fl_i.html | 16 ++++--
build/emd_Fl_ief.html | 16 ++++--
build/emd_Me.html | 10 +++-
build/emd_Me_Me.html | 16 ++++--
build/emd_Me_dc.html | 14 +++--
build/emd_Me_ebM.html | 10 +++-
build/emd_Me_mc.html | 10 +++-
build/emd_ce.html | 18 +++---
build/emd_ce_amom.html | 12 ++--
build/emd_ce_ce.html | 12 ++--
build/emd_ce_mom.html | 14 +++--
build/emd_ce_mst.html | 16 ++++--
build/emd_ce_poy.html | 22 +++++---
build/emd_emw.html | 18 +++---
build/emd_emw_ep.html | 14 +++--
build/emd_emw_mpw.html | 12 ++--
build/emd_emw_we.html | 12 ++--
build/emdm.html | 10 +++-
build/emdm_Me.html | 10 +++-
build/emdm_Me_Mem.html | 26 +++++----
build/emdm_Me_bc.html | 12 ++--
build/emdm_emwm.html | 10 +++-
build/emdm_emwm_ad.html | 10 +++-
build/emdm_emwm_ad_c.html | 10 +++-
build/emdm_emwm_plm.html | 12 ++--
build/emdm_emwm_refl.html | 10 +++-
build/emdm_emwm_refl_Ba.html | 10 +++-
build/emdm_emwm_refl_Fe.html | 10 +++-
build/emdm_emwm_refl_ni.html | 10 +++-
build/emdm_emwm_refl_oi.html | 18 +++---
build/emdm_emwm_refr.html | 10 +++-
build/emdm_emwm_wg.html | 10 +++-
build/emdm_emwm_wg_c.html | 10 +++-
build/emdm_emwm_wg_gw.html | 10 +++-
build/emdm_emwm_wg_r.html | 10 +++-
build/emf.html | 18 +++---
build/emf_g.html | 10 +++-
build/emf_g_Cg.html | 10 +++-
build/emf_g_Lg.html | 14 +++--
build/emf_svp.html | 18 +++---
build/ems.html | 10 +++-
build/ems_ca.html | 18 +++---
build/ems_ca_fe.html | 18 +++---
build/ems_ca_fe_L.html | 12 ++--
build/ems_ca_fe_g.html | 14 +++--
build/ems_ca_fe_uP.html | 14 +++--
build/ems_ca_me.html | 10 +++-
build/ems_ca_me_Ed.html | 10 +++-
build/ems_ca_me_Eq.html | 10 +++-
build/ems_ca_me_a.html | 10 +++-
build/ems_ca_me_h.html | 18 +++---
build/ems_ca_me_md.html | 14 +++--
build/ems_ca_mi.html | 10 +++-
build/ems_ca_mi_fe.html | 10 +++-
build/ems_ca_mi_isc.html | 10 +++-
build/ems_ca_mi_o.html | 10 +++-
build/ems_ca_sv.html | 10 +++-
build/ems_ca_sv_car.html | 14 +++--
build/ems_ca_sv_cyl.html | 10 +++-
build/ems_ca_sv_sph.html | 18 +++---
build/ems_es.html | 18 +++---
build/ems_es_c.html | 10 +++-
build/ems_es_c_cap.html | 12 ++--
build/ems_es_c_ic.html | 12 ++--
build/ems_es_c_p.html | 12 ++--
build/ems_es_c_sc.html | 10 +++-
build/ems_es_e.html | 10 +++-
build/ems_es_e_c.html | 10 +++-
build/ems_es_e_ccd.html | 14 +++--
build/ems_es_e_pcd.html | 10 +++-
build/ems_es_ec.html | 10 +++-
build/ems_es_ec_b.html | 10 +++-
build/ems_es_ec_c.html | 10 +++-
build/ems_es_ec_q.html | 10 +++-
build/ems_es_ec_s.html | 10 +++-
build/ems_es_ef.html | 10 +++-
build/ems_es_ef_Gl.html | 32 ++++++-----
build/ems_es_ef_cE.html | 22 +++++---
build/ems_es_ef_ccd.html | 32 ++++++-----
build/ems_es_ef_pc.html | 24 ++++----
build/ems_es_efo.html | 10 +++-
build/ems_es_efo_cl.html | 20 ++++---
build/ems_es_efo_e.html | 22 ++++++--
build/ems_es_efo_exp.html | 26 +++++----
build/ems_es_efo_ps.html | 12 ++--
build/ems_es_ep.html | 10 +++-
build/ems_es_ep_PL.html | 14 +++--
build/ems_es_ep_bc.html | 10 +++-
build/ems_es_ep_c.html | 10 +++-
build/ems_es_ep_d.html | 22 +++++---
build/ems_es_ep_ex.html | 14 +++--
build/ems_es_ep_fp.html | 12 ++--
build/ems_ms.html | 18 +++---
build/ems_ms_BS.html | 10 +++-
build/ems_ms_BS_sc.html | 18 +++---
build/ems_ms_dcB.html | 10 +++-
build/ems_ms_dcB_BS.html | 24 ++++----
build/ems_ms_dcB_sc.html | 12 ++--
build/ems_ms_lf.html | 10 +++-
build/ems_ms_lf_c.html | 14 +++--
build/ems_ms_lf_pc.html | 18 +++---
build/ems_ms_vp.html | 24 ++++----
build/ems_ms_vp_LC.html | 12 ++--
build/ems_ms_vp_comp.html | 10 +++-
build/ems_ms_vp_mbc.html | 16 ++++--
build/ems_ms_vp_me.html | 18 +++---
build/emsm.html | 18 +++---
build/emsm_esm.html | 12 ++--
build/emsm_esm_D.html | 20 ++++---
build/emsm_esm_D_bc.html | 12 ++--
build/emsm_esm_di.html | 14 +++--
build/emsm_esm_di_ld.html | 36 ++++++------
build/emsm_esm_fpo.html | 20 ++++---
build/emsm_esm_fpo_fid.html | 12 ++--
build/emsm_esm_fpo_pibc.html | 10 +++-
build/emsm_esm_p.html | 16 ++++--
build/emsm_esm_s.html | 10 +++-
build/emsm_msm.html | 18 +++---
build/emsm_msm_H.html | 10 +++-
build/emsm_msm_H_A.html | 18 +++---
build/emsm_msm_a.html | 10 +++-
build/emsm_msm_fmo.html | 10 +++-
build/emsm_msm_fmo_bc.html | 20 ++++---
build/emsm_msm_fmo_fim.html | 10 +++-
build/emsm_msm_fmo_pibc.html | 10 +++-
build/emsm_msm_lnlm.html | 10 +++-
build/emsm_msm_lnlm_fm.html | 10 +++-
build/emsm_msm_lnlm_sp.html | 12 ++--
build/emsm_msm_m.html | 10 +++-
build/emsm_msm_m_dpf.html | 14 +++--
build/emsm_msm_m_fdi.html | 14 +++--
build/in.html | 10 +++-
build/in_p.html | 33 ++++++++++-
build/in_t.html | 13 +++--
build/in_t_c.html | 40 +++++++------
build/index.html | 13 +++--
build/qed.html | 10 +++-
build/qed_t.html | 10 +++-
build/red.html | 18 +++---
build/red_rem.html | 10 +++-
build/red_rem_Fmunu.html | 16 ++++--
build/red_rem_Ltf.html | 12 ++--
build/red_rem_Me.html | 22 +++++---
build/red_rem_mre.html | 12 ++--
build/red_rm.html | 10 +++-
build/red_rm_Mf.html | 16 ++++--
build/red_rm_pt.html | 14 +++--
build/red_rm_rme.html | 18 +++---
build/red_sr.html | 10 +++-
build/red_sr_4v.html | 16 ++++--
build/red_sr_Lt.html | 12 ++--
build/red_sr_p.html | 14 +++--
207 files changed, 1882 insertions(+), 1097 deletions(-)
diff --git a/build/a.html b/build/a.html
index 386f17d..a1c9672 100644
--- a/build/a.html
+++ b/build/a.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1629,7 +1633,7 @@ Table of contents
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/a_l.html b/build/a_l.html
index ed50e09..46771ad 100644
--- a/build/a_l.html
+++ b/build/a_l.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1712,7 +1716,7 @@ Wiley, 1986 [2nd edition]
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c.html b/build/c.html
index e5f2d8d..3f1a057 100644
--- a/build/c.html
+++ b/build/c.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1629,7 +1633,7 @@ Table of contents
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m.html b/build/c_m.html
index 2103581..1e87a4c 100644
--- a/build/c_m.html
+++ b/build/c_m.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1635,7 +1639,7 @@ Table of contents
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_cs.html b/build/c_m_cs.html
index 0baaa19..c1751dd 100644
--- a/build/c_m_cs.html
+++ b/build/c_m_cs.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1631,7 +1635,7 @@ Table of contents
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_cs_cyl.html b/build/c_m_cs_cyl.html
index dcd94f1..ac082c7 100644
--- a/build/c_m_cs_cyl.html
+++ b/build/c_m_cs_cyl.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1622,47 +1626,39 @@ Table of contents
\((r, \phi, z)\). Relation to Cartesian coordinates:
-
-\[
+\begin{equation}
x = r \cos \phi, y = r \sin \phi, z = z
\label{Gr(1.74)}
-\]
-
+\end{equation}
The unit vectors are
-
-\[
+\begin{equation}
\hat{\bf r} = \cos \phi ~\hat{\bf x} + \sin \phi~\hat{\bf y},
\hat{\boldsymbol \phi} = -\sin \theta ~\hat{\bf x} + \cos \phi~\hat{\bf y},
\hat{\bf z} = \hat{\bf z}.
\label{Gr(1.75)}
-\]
-
+\end{equation}
Infinitesimal displacement:
-
-\[
+\begin{equation}
d{\bf l} = dr ~\hat{\bf r} + r d\phi~\hat{\boldsymbol \phi} + dz ~\hat{\bf z}.
\label{Gr(1.77)}
-\]
-
+\end{equation}
Volume element:
-
-\[
+\begin{equation}
d\tau = r dr d\phi dz
\label{Gr(1.78)}
-\]
-
+\end{equation}
Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in ]-\infty, \infty[\).
@@ -1672,14 +1668,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
-
+
-
+
@@ -1688,32 +1684,26 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
-
-\[
-{\boldsymbol ∇} T = \frac{\partial T}{\partial r}~\hat{\bf r}
-
-
-\frac{1}{r} \frac{\partial T}{\partial \phi}~\hat{\boldsymbol \phi}
-\frac{\partial T}{\partial z} ~\hat{\bf z}
-
-
+\begin{equation}
+{\boldsymbol \nabla} T = \frac{\partial T}{\partial r}~\hat{\bf r}
++ \frac{1}{r} \frac{\partial T}{\partial \phi}~\hat{\boldsymbol \phi}
++ \frac{\partial T}{\partial z} ~\hat{\bf z}
\tag{cylgrad}\label{cylgrad}
-\]
-
+\end{equation}
-
+
-
+
@@ -1722,32 +1712,26 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
-
-\[
-{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r} \frac{\partial}{\partial r} (r v_r)
-
-
-\frac{1}{r} \frac{∂ v_{φ}}{∂ φ} + \frac{\partial v_z}{\partial z}.
-
-
+\begin{equation}
+{\boldsymbol \nabla} \cdot {\bf v} = \frac{1}{r} \frac{\partial}{\partial r} (r v_r)
++ \frac{1}{r} \frac{\partial v_{\phi}}{\partial \phi} + \frac{\partial v_z}{\partial z}.
\tag{cyl_div}
\label{cyl_div}
-\]
-
+\end{equation}
-
+
-
+
@@ -1756,36 +1740,24 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
-
-\[
-{\boldsymbol ∇} × {\bf v} = \left( \frac{1}{r} \frac{\partial v_z}{\partial \phi} - \frac{∂ v_{φ}}{∂ z}\right) ~\hat{\bf r}
-
-
-\left( \frac{\partial v_r}{\partial z} - \frac{\partial v_z}{\partial r} \right) ~\hat{\boldsymbol \phi}
-\frac{1}{r} \left( \frac{\partial}{\partial r} (r v_{φ}) - \frac{\partial v_r}{\partial \phi} \right) ~\hat{\bf z}
-
-
+\begin{align}
+{\boldsymbol \nabla} \times {\bf v} = \left( \frac{1}{r} \frac{\partial v_z}{\partial \phi} - \frac{\partial v_{\phi}}{\partial z}\right) ~\hat{\bf r}
++ \left( \frac{\partial v_r}{\partial z} - \frac{\partial v_z}{\partial r} \right) ~\hat{\boldsymbol \phi} \nonumber \\
++ \frac{1}{r} \left( \frac{\partial}{\partial r} (r v_{\phi}) - \frac{\partial v_r}{\partial \phi} \right) ~\hat{\bf z}
\tag{cyl_curl}
\label{cyl_curl}
-\]
-
+\end{align}
-
-\[
-{\boldsymbol ∇}^2 T = \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial T}{\partial r} \right)
-
-
-\frac{1}{r^2} \frac{\partial^2 T}{\partial \phi^2} + \frac{\partial^2 T}{\partial z^2}
-
-
+\begin{equation}
+{\boldsymbol \nabla}^2 T = \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial T}{\partial r} \right)
++ \frac{1}{r^2} \frac{\partial^2 T}{\partial \phi^2} + \frac{\partial^2 T}{\partial z^2}
\label{Gr(1.82)}
-\]
-
+\end{equation}
@@ -1795,7 +1767,7 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_cs_hyp.html b/build/c_m_cs_hyp.html
index 6342d80..f36ae93 100644
--- a/build/c_m_cs_hyp.html
+++ b/build/c_m_cs_hyp.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1624,7 +1628,7 @@ Table of contents
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_cs_sph.html b/build/c_m_cs_sph.html
index c46a505..c854513 100644
--- a/build/c_m_cs_sph.html
+++ b/build/c_m_cs_sph.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1688,70 +1692,46 @@ Infinitesimal surface element: depends on situation.
-
-\[
-{\boldsymbol ∇} T = \frac{\partial T}{\partial r} \hat{\boldsymbol r} + \frac{1}{r} \frac{\partial T}{\partial \theta} \hat{\boldsymbol \theta}
-
-
-\frac{1}{r\sin \theta} \frac{\partial T}{\partial \phi} \hat{\boldsymbol \phi}.
-
-
+\begin{equation}
+{\boldsymbol \nabla} T = \frac{\partial T}{\partial r} \hat{\boldsymbol r} + \frac{1}{r} \frac{\partial T}{\partial \theta} \hat{\boldsymbol \theta}
++ \frac{1}{r\sin \theta} \frac{\partial T}{\partial \phi} \hat{\boldsymbol \phi}.
\label{Gr(1.70)}
-\]
-
+\end{equation}
-
-\[
-{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 v_r) + \frac{1}{r\sin \theta} \frac{\partial}{\partial \theta} (sinθ v_{θ})
-
-
-\frac{1}{r \sin \theta} \frac{∂ v_{φ}}{∂ φ}
-
-
+\begin{equation}
+{\boldsymbol \nabla} \cdot {\bf v} = \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 v_r) + \frac{1}{r\sin \theta} \frac{\partial}{\partial \theta} (\sin\theta v_{\theta})
++ \frac{1}{r \sin \theta} \frac{\partial v_{\phi}}{\partial \phi}
\label{Gr(1.71)}
-\]
-
+\end{equation}
-
-\[
-{\boldsymbol ∇} × {\bf v} = \frac{1}{r\sin \theta} \left[ \frac{\partial}{\partial \theta} (sin θ v_{φ}) - \frac{∂ v_{θ}}{∂ φ} \right] \hat{\bf r}
-
-
-\frac{1}{r} \left[ \frac{1}{\sin \theta} \frac{\partial v_r}{\partial \phi} - \frac{\partial}{\partial r} (r v_{φ}) \right] \hat{\boldsymbol \theta}
-\frac{1}{r} \left[ \frac{\partial}{\partial r} (r v_{θ}) - \frac{\partial v_r}{\partial \theta} \right] \hat{\boldsymbol \phi}
-
-
+\begin{equation}
+{\boldsymbol \nabla} \times {\bf v} = \frac{1}{r\sin \theta} \left[ \frac{\partial}{\partial \theta} (\sin \theta v_{\phi}) - \frac{\partial v_{\theta}}{\partial \phi} \right] \hat{\bf r}
++ \frac{1}{r} \left[ \frac{1}{\sin \theta} \frac{\partial v_r}{\partial \phi} - \frac{\partial}{\partial r} (r v_{\phi}) \right] \hat{\boldsymbol \theta}
++ \frac{1}{r} \left[ \frac{\partial}{\partial r} (r v_{\theta}) - \frac{\partial v_r}{\partial \theta} \right] \hat{\boldsymbol \phi}
\label{Gr(1.72)}
-\]
-
+\end{equation}
-
-\[
-{\boldsymbol ∇}^2 T = \frac{1}{r^2} \frac{\partial}{\partial r} \left(r^2 \frac{\partial T}{\partial r}\right)
-
-
-\frac{1}{r^2 \sin \theta} \frac{\partial}{\partial \theta} \left( sin θ \frac{\partial T}{\partial \theta}\right)
-\frac{1}{r^2 \sin^2 \theta} \frac{\partial^2 T}{\partial \phi^2}
-
-
+\begin{equation}
+{\boldsymbol \nabla}^2 T = \frac{1}{r^2} \frac{\partial}{\partial r} \left(r^2 \frac{\partial T}{\partial r}\right)
++ \frac{1}{r^2 \sin \theta} \frac{\partial}{\partial \theta} \left( \sin \theta \frac{\partial T}{\partial \theta}\right)
++ \frac{1}{r^2 \sin^2 \theta} \frac{\partial^2 T}{\partial \phi^2}
\label{Gr(1.73)}
-\]
-
+\end{equation}
@@ -1761,7 +1741,7 @@ Infinitesimal surface element: depends on situation.
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_dc.html b/build/c_m_dc.html
index 7672054..29d8848 100644
--- a/build/c_m_dc.html
+++ b/build/c_m_dc.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1634,7 +1638,7 @@ Table of contents
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_dc_curl.html b/build/c_m_dc_curl.html
index 55e5cdf..fb804be 100644
--- a/build/c_m_dc_curl.html
+++ b/build/c_m_dc_curl.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1636,7 +1640,7 @@ v_x & v_y & v_z \end{array} \right| \nonumber \\
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_dc_d2.html b/build/c_m_dc_d2.html
index cf3310e..f286af4 100644
--- a/build/c_m_dc_d2.html
+++ b/build/c_m_dc_d2.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1620,9 +1624,9 @@ Table of contents
-
-
-
+
+
+
\({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) 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
@@ -1631,36 +1635,36 @@ given by the Laplacian of the corresponding vector elements.
-
-
-
+
-
-
-
+
+
+
\({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name.
-
-
-
+
-
-
-
+
+
+
\[
{\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v}
@@ -1674,7 +1678,7 @@ This always vanishes.
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_dc_del.html b/build/c_m_dc_del.html
index 646c045..38c6237 100644
--- a/build/c_m_dc_del.html
+++ b/build/c_m_dc_del.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1635,7 +1639,7 @@ The del/grad/nabla operator is defined as
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_dc_div.html b/build/c_m_dc_div.html
index 4609351..baad0fe 100644
--- a/build/c_m_dc_div.html
+++ b/build/c_m_dc_div.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1632,7 +1636,7 @@ Table of contents
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_dc_g.html b/build/c_m_dc_g.html
index 30a343d..32a09f6 100644
--- a/build/c_m_dc_g.html
+++ b/build/c_m_dc_g.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1656,7 +1660,7 @@ is a vector called the gradient of \(T\).
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_dc_pr.html b/build/c_m_dc_pr.html
index e4b8301..4f01eb3 100644
--- a/build/c_m_dc_pr.html
+++ b/build/c_m_dc_pr.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1629,7 +1633,7 @@ Six product rules (on inside front cover of Gr).
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_dd.html b/build/c_m_dd.html
index 8c833ed..b47001d 100644
--- a/build/c_m_dd.html
+++ b/build/c_m_dd.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1631,7 +1635,7 @@ Table of contents
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_dd_1d.html b/build/c_m_dd_1d.html
index e7d8a81..ea993df 100644
--- a/build/c_m_dd_1d.html
+++ b/build/c_m_dd_1d.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1643,7 +1647,7 @@ Consequences: for any smooth differentiable function \(f(x)\),
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_dd_3d.html b/build/c_m_dd_3d.html
index 5915f4f..ea8ad45 100644
--- a/build/c_m_dd_3d.html
+++ b/build/c_m_dd_3d.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1618,43 +1622,37 @@ Table of contents
c.m.dd.3d
-
-\[
+\begin{equation}
\delta^{(3)} ({\bf r} - {\bf r}') = \delta (x - x') \delta (y - y') \delta (z - z')
\label{Gr(1.96)}
-\]
-
+\end{equation}
-
-\[
+\begin{equation}
\int d\tau f({\bf r}) \delta^{(3)} ({\bf r} - {\bf a}) = f({\bf a})
\label{Gr(1.97)}
-\]
-
+\end{equation}
Resolution of divergence of \(\hat{\bf r}/r^2\) paradox:
-
-\[
+\begin{equation}
{\boldsymbol \nabla} \cdot \left(\frac{\hat{\bf r}}{r^2} \right)= 4\pi \delta^{(3)} ({\bf r}).
\label{Gr(1.99)}
-\]
-
+\end{equation}
More generally,
-
+
-
+
@@ -1662,43 +1660,37 @@ More generally,
-
-\[
+\begin{equation}
\boxed{
{\boldsymbol \nabla} \cdot \left(\frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3} \right)= 4\pi \delta^{(3)} ({\bf r}).
}
\tag{divdel}\label{divdel}
-\]
-
+\end{equation}
Since
-
-\[
+\begin{equation}
{\boldsymbol \nabla}_1 \left(\frac{1}{r_{12}}\right) = -\frac{\hat{\bf r}_{12}}{r_{12}^2}
\label{Gr(1.101)}
-\]
-
+\end{equation}
we have that
-
-\[
+\begin{equation}
{\boldsymbol \nabla}^2 \left( \frac{1}{|{\bf r} - {\bf r}'|} \right) = -4\pi \delta^{(3)} ({\bf r} - {\bf r}')
\label{Gr(1.102)}
-\]
-
+\end{equation}
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_dd_div.html b/build/c_m_dd_div.html
index 8e8c87f..89ff57d 100644
--- a/build/c_m_dd_div.html
+++ b/build/c_m_dd_div.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1622,12 +1626,10 @@ Table of contents
Try to calculate this directly:
-
-\[
+\begin{equation}
{\boldsymbol \nabla} \cdot \frac{\hat{\bf r}}{r^2} = \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{1}{r^2}\right) =^{?} 0
\label{Gr(1.84)}
-\]
-
+\end{equation}
Now apply the divergence theorem.
@@ -1635,16 +1637,14 @@ Integrate over a sphere of radius \(R\) centered at the origin (Prob. 1.38b):
-
-\[
+\begin{equation}
\oint \frac{\hat{\bf r}}{r^2} \cdot d{\bf a} = \int \left(\frac{1}{R^2} \hat{\bf r} \right) \cdot \left( R^2 \sin \theta d\theta d\phi ~\hat{\bf r} \right)
= \int_0^{\pi} d\theta \sin \theta \int_0^{2\pi} d\phi = 4\pi
\label{Gr(1.85)}
-\]
-
+\end{equation}
-Problem: in (1.84), we've divided by zero when \(r = 0\).
+Problem: in Gr(1.84), we've divided by zero when \(r = 0\).
@@ -1653,7 +1653,7 @@ Problem: in (1.84), we've divided by zero when \(r = 0\).
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_ic.html b/build/c_m_ic.html
index 75eb64e..51a6fa2 100644
--- a/build/c_m_ic.html
+++ b/build/c_m_ic.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1634,7 +1638,7 @@ Table of contents
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_ic_ftc.html b/build/c_m_ic_ftc.html
index 6fe777d..79f9b98 100644
--- a/build/c_m_ic_ftc.html
+++ b/build/c_m_ic_ftc.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1632,7 +1636,7 @@ Table of contents
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_ic_ftg.html b/build/c_m_ic_ftg.html
index 3a0456a..cd89d0d 100644
--- a/build/c_m_ic_ftg.html
+++ b/build/c_m_ic_ftg.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1641,7 +1645,7 @@ Table of contents
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_ic_gauss.html b/build/c_m_ic_gauss.html
index e9464e8..8d6179c 100644
--- a/build/c_m_ic_gauss.html
+++ b/build/c_m_ic_gauss.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1635,7 +1639,7 @@ This is know either as Gauss' theorem , Green's theorem or the d
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_ic_ip.html b/build/c_m_ic_ip.html
index 9a18cf9..a23eb7c 100644
--- a/build/c_m_ic_ip.html
+++ b/build/c_m_ic_ip.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1642,7 +1646,7 @@ or in other words
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_ic_lsv.html b/build/c_m_ic_lsv.html
index fde2ff3..9b89b48 100644
--- a/build/c_m_ic_lsv.html
+++ b/build/c_m_ic_lsv.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1620,9 +1624,9 @@ Table of contents
-
-
-
+
+
+
\[
{\int_{\bf a}^{\bf b}}_{\cal P} {\bf v} \cdot d{\bf l}
@@ -1651,9 +1655,9 @@ Integral over a closed loop:
-
-
-
+
+
+
\[
\int_{\cal S} {\bf v} \cdot d{\bf a}
@@ -1673,9 +1677,9 @@ Over a closed surface:
-
-
-
+
+
+
\[
\int_{\cal V} T d\tau
@@ -1703,7 +1707,7 @@ d\tau = dx dy dz
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_ic_stokes.html b/build/c_m_ic_stokes.html
index be76a7a..5507208 100644
--- a/build/c_m_ic_stokes.html
+++ b/build/c_m_ic_stokes.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1618,14 +1622,14 @@ Table of contents
c.m.ic.stokes
-
+
-
+
@@ -1657,7 +1661,7 @@ the boundary shrinks to a point.
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/c_m_uf.html b/build/c_m_uf.html
index 879c3a6..183c63e 100644
--- a/build/c_m_uf.html
+++ b/build/c_m_uf.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
@@ -1678,7 +1680,7 @@ The following conditions are equivalent:
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/d.html b/build/d.html
index 05262db..2d2f82a 100644
--- a/build/d.html
+++ b/build/d.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1619,8 +1623,8 @@ Table of contents
d
-
-
+
+
Objectives
@@ -1671,7 +1675,7 @@ I have little doubt you'll pass the course.
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/d_emd.html b/build/d_emd.html
index 1b899c8..fbbcec6 100644
--- a/build/d_emd.html
+++ b/build/d_emd.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1651,7 +1655,7 @@ As a strict minimum, you should be able to:
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/d_emd_ce.html b/build/d_emd_ce.html
index 6c6bb5e..53435fc 100644
--- a/build/d_emd_ce.html
+++ b/build/d_emd_ce.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1646,7 +1650,7 @@ As a strict minimum, you should be able to:
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/d_emd_emw.html b/build/d_emd_emw.html
index bec85f1..ff868bc 100644
--- a/build/d_emd_emw.html
+++ b/build/d_emd_emw.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1649,7 +1653,7 @@ As a strict minimum, you should be able to:
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/d_emf.html b/build/d_emf.html
index 9bba6fa..7fc5719 100644
--- a/build/d_emf.html
+++ b/build/d_emf.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1646,7 +1650,7 @@ As a strict minimum, you should be able to:
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/d_ems.html b/build/d_ems.html
index cb083bb..31de60e 100644
--- a/build/d_ems.html
+++ b/build/d_ems.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1668,7 +1672,7 @@ As a strict minimum, you should be able to:
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/d_ems_ca.html b/build/d_ems_ca.html
index 937ed32..d775891 100644
--- a/build/d_ems_ca.html
+++ b/build/d_ems_ca.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1651,7 +1655,7 @@ a point source charge \(q\) at \({\bf r}_s\) with an infinite grounded conductin
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/d_ems_ms.html b/build/d_ems_ms.html
index 957080c..ba8a9f6 100644
--- a/build/d_ems_ms.html
+++ b/build/d_ems_ms.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1648,7 +1652,7 @@ As a strict minimum, you should be able to:
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/d_emsm.html b/build/d_emsm.html
index 9603293..ecdd13e 100644
--- a/build/d_emsm.html
+++ b/build/d_emsm.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1651,7 +1655,7 @@ As a strict minimum, you should be able to:
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/d_emsm_msm.html b/build/d_emsm_msm.html
index 7430bf3..2221e8e 100644
--- a/build/d_emsm_msm.html
+++ b/build/d_emsm_msm.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1649,7 +1653,7 @@ As a strict minimum, you should be able to:
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/d_m.html b/build/d_m.html
index e439a56..0b48535 100644
--- a/build/d_m.html
+++ b/build/d_m.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1659,7 +1663,7 @@ Things you should be able to do (ideally: from scratch, on a blank sheet of pape
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/d_red.html b/build/d_red.html
index 6455be5..5ce716c 100644
--- a/build/d_red.html
+++ b/build/d_red.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1653,7 +1657,7 @@ As a strict minimum, you should be able to:
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/emd.html b/build/emd.html
index cccc3f1..e88ec90 100644
--- a/build/emd.html
+++ b/build/emd.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1619,8 +1623,8 @@ Table of contents
emd
-
-
+
+
Prerequisites
@@ -1629,8 +1633,8 @@ Prerequisites
-
-
+
+
Objectives
@@ -1658,7 +1662,7 @@ Objectives
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/emd_Fl.html b/build/emd_Fl.html
index 715cce4..697b018 100644
--- a/build/emd_Fl.html
+++ b/build/emd_Fl.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1632,7 +1636,7 @@ Table of contents
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/emd_Fl_Fl.html b/build/emd_Fl_Fl.html
index f9da649..eea9f62 100644
--- a/build/emd_Fl_Fl.html
+++ b/build/emd_Fl_Fl.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1659,7 +1663,7 @@ Empirically: the changing magnetic field induces an electric current around
the circuit. This current is really driven by an electric field having a component
along the wire. The line integral of this field is called the
-
+
Electromotive force (or electromotance) ,
\[
@@ -1681,7 +1685,7 @@ to the rate of change of the magnetic flux,
\]
so we obtain
-
+
Faraday's law (integral form N.B.: for a stationary loop )
\[
@@ -1699,7 +1703,7 @@ for any loop (on a wire or not). Using Stokes' theorem,
\]
we obtain
-
+
Faraday's law (differential form)
\[
@@ -1723,7 +1727,7 @@ to an opposing counter-reaction.
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/emd_Fl_e.html b/build/emd_Fl_e.html
index bd0874e..f4da0de 100644
--- a/build/emd_Fl_e.html
+++ b/build/emd_Fl_e.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1678,7 +1682,7 @@ W = \frac{1}{2\mu_0} \left[ \int_{\cal V} d\tau B^2 - \int_{\cal V} d\tau {\bold
\]
We can integrate over all space: after neglecting boundary terms (assuming fields fall to zero at infinity), we are left with
-
+
\[
W_{mag} = \frac{1}{2\mu_0} \int d\tau B^2
@@ -1699,7 +1703,7 @@ W_{mag} = \frac{1}{2} \int d\tau ({\bf A} \cdot {\bf J}) = \frac{1}{2\mu_0} \int
\hspace{2cm} \mbox{(7.31 and 7.34)}
\end{align}
-
+
\paragraph{Example 7.13:} coaxial cable (inner cylinder radius \(a\), outer \(b\)) carries current \(I\).
Find energy stored in section of length \(l\).
@@ -1725,7 +1729,7 @@ Note: gives easy way to find inductance, since \(W = \frac{1}{2} L I^2\).
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/emd_Fl_i.html b/build/emd_Fl_i.html
index eda2671..7150747 100644
--- a/build/emd_Fl_i.html
+++ b/build/emd_Fl_i.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1658,7 +1662,7 @@ M_{12} = M_{21}
\]
-
+
\paragraph{Example 7.10:}
short solenoid (length \(l\), radius \(a\), \(n_1\) turns per unit length) lies concentrically inside
@@ -1708,7 +1712,7 @@ Inductance: measured in {\bf henries} (\(H\)). \(H = V s/A\).
-
+
\paragraph{Example 7.11:} find self-inductance of toroidal coil with
rectangular cross-section (inner radius \(a\), outer radius \(b\), height \(h\))
@@ -1735,7 +1739,7 @@ Total flux: \(N\) times this, so self-inductance is
Inductance (like capacitance) is intrinsically positive. Use Lenz law. Think of {\bf back EMF}.
-
+
\paragraph{Example 7.12:} circuit with inductance \(L\), resistor \(R\) and battery \({\cal E}_0\).
What is the current ?
@@ -1761,7 +1765,7 @@ where \(\tau \equiv L/R\) is the {\bf time constant} of the circuit.
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/emd_Fl_ief.html b/build/emd_Fl_ief.html
index 9246b27..b54f403 100644
--- a/build/emd_Fl_ief.html
+++ b/build/emd_Fl_ief.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents
+Section and equation labelling in.t.l
+
+
+
Contextual colors in.t.c
@@ -736,7 +740,7 @@ Table of contents
-Dielectrics emsm.esm.d
+Dielectrics emsm.esm.di
@@ -1642,7 +1646,7 @@ law in integral form:
-
+
{\bf Example 7.7:}
\({\bf B}(t)\) points up in circular region of radius \(R\). What is the induced \({\bf E}(t)\) ?
@@ -1658,7 +1662,7 @@ Increasing \({\bf B}\): clockwise (viewed from above) \({\bf E}\) from Lenz.
-
+
{\bf Example 7.8:} wheel or radius \(b\) with line charge \(\lambda\) on the rim.
Uniform magnetic field \({\bf B}_0\) in central region up to \(a < b\),
@@ -1692,7 +1696,7 @@ called the {\bf quasistatic} approximation, and works provided we deal with
'slow enough' phenomena.
-
+
{\bf Example 7.9:} infinitely long straight wire carries \(I(t)\). Find
induced \({\bf E}\) field as a function of distance \(s\) from wire.
@@ -1727,7 +1731,7 @@ Reason: in this case, we've overstepped the quasistatic limit. We need
Author: Jean-Sébastien Caux
-
Created: 2022-02-08 Tue 06:55
+
Created: 2022-02-08 Tue 17:21
Validate
diff --git a/build/emd_Me.html b/build/emd_Me.html
index 849eb15..2d9750c 100644
--- a/build/emd_Me.html
+++ b/build/emd_Me.html
@@ -1,7 +1,7 @@
-
+
Pre-Quantum Electrodynamics
@@ -272,6 +272,10 @@ Table of contents