{\bf Angular momentum of EM fields} \[ @@ -1625,7 +1654,7 @@ target="_blank">Creative Commons Attribution 4.0 International License.
Created: 2022-02-21 Mon 10:33
+Created: 2022-02-21 Mon 20:41
- -Polarizationemsm.esm.p - - -
- -Dielectricsemsm.esm.di - - -
-
+
-The Field of a Polarized Objectemsm.esm.fpo +Matter Bathed in E Fields; Polarizationemsm.esm.mE
- -Physical Interpretation of Bound Chargesemsm.esm.fpo.pibc +Overviewemsm.esm.mE.o
- -The Field Inside a Dielectricemsm.esm.fpo.fid +Polarizationemsm.esm.mE.P + + + +
+ -
+
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+Polarized Objects; Bound Chargesemsm.esm.po + + +
+-
+
- +Physical Interpretation of Bound Chargesemsm.esm.po.pibc + + +
- +The Field Inside a Dielectricemsm.esm.po.fid @@ -750,18 +763,34 @@ Table of contents
+ - +Dielectricsemsm.esm.di +
-
-Dielectricsemsm.esm.di +Linear Dielectricsemsm.esm.ld
- -Linear Dielectricsemsm.esm.di.ld +Susceptibility, Permittivity, Dielectric Constantemsm.esm.ld.sp + + +
- +Boundary Value Problems with Linear Dielectricsemsm.esm.ld.bvp + + +
- +Energy in Dielectric Systemsemsm.esm.ld.e + + +
- +Forces on Dielectricsemsm.esm.ld.f @@ -1614,7 +1643,7 @@ This means that \] Since this is true for any volume, we have (re)derived the -
- -Polarizationemsm.esm.p - - -
- -Dielectricsemsm.esm.di - - -
-
+
-The Field of a Polarized Objectemsm.esm.fpo +Matter Bathed in E Fields; Polarizationemsm.esm.mE
- -Physical Interpretation of Bound Chargesemsm.esm.fpo.pibc +Overviewemsm.esm.mE.o
- -The Field Inside a Dielectricemsm.esm.fpo.fid +Polarizationemsm.esm.mE.P + + + +
+ -
+
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+Polarized Objects; Bound Chargesemsm.esm.po + + +
+-
+
- +Physical Interpretation of Bound Chargesemsm.esm.po.pibc + + +
- +The Field Inside a Dielectricemsm.esm.po.fid @@ -750,18 +763,34 @@ Table of contents
+ - +Dielectricsemsm.esm.di +
-
-Dielectricsemsm.esm.di +Linear Dielectricsemsm.esm.ld
- -Linear Dielectricsemsm.esm.di.ld +Susceptibility, Permittivity, Dielectric Constantemsm.esm.ld.sp + + +
- +Boundary Value Problems with Linear Dielectricsemsm.esm.ld.bvp + + +
- +Energy in Dielectric Systemsemsm.esm.ld.e + + +
- +Forces on Dielectricsemsm.esm.ld.f @@ -1607,7 +1636,7 @@ in which the first integral can be interpreted as the momentum stored in the EM
- -Polarizationemsm.esm.p - - -
- -Dielectricsemsm.esm.di - - -
-
+
-The Field of a Polarized Objectemsm.esm.fpo +Matter Bathed in E Fields; Polarizationemsm.esm.mE
- -Physical Interpretation of Bound Chargesemsm.esm.fpo.pibc +Overviewemsm.esm.mE.o
- -The Field Inside a Dielectricemsm.esm.fpo.fid +Polarizationemsm.esm.mE.P + + + +
+ -
+
+++
+Polarized Objects; Bound Chargesemsm.esm.po + + +
+-
+
- +Physical Interpretation of Bound Chargesemsm.esm.po.pibc + + +
- +The Field Inside a Dielectricemsm.esm.po.fid @@ -750,18 +763,34 @@ Table of contents
+ - +Dielectricsemsm.esm.di +
-
-Dielectricsemsm.esm.di +Linear Dielectricsemsm.esm.ld
- -Linear Dielectricsemsm.esm.di.ld +Susceptibility, Permittivity, Dielectric Constantemsm.esm.ld.sp + + +
- +Boundary Value Problems with Linear Dielectricsemsm.esm.ld.bvp + + +
- +Energy in Dielectric Systemsemsm.esm.ld.e + + +
- +Forces on Dielectricsemsm.esm.ld.f @@ -1649,7 +1678,7 @@ and similarly for \({\boldsymbol B}\). We thus get
- -Polarizationemsm.esm.p - - -
- -Dielectricsemsm.esm.di - - -
-
+
-The Field of a Polarized Objectemsm.esm.fpo +Matter Bathed in E Fields; Polarizationemsm.esm.mE
- -Physical Interpretation of Bound Chargesemsm.esm.fpo.pibc +Overviewemsm.esm.mE.o
- -The Field Inside a Dielectricemsm.esm.fpo.fid +Polarizationemsm.esm.mE.P + + + +
+ -
+
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+Polarized Objects; Bound Chargesemsm.esm.po + + +
+-
+
- +Physical Interpretation of Bound Chargesemsm.esm.po.pibc + + +
- +The Field Inside a Dielectricemsm.esm.po.fid @@ -750,18 +763,34 @@ Table of contents
+ - +Dielectricsemsm.esm.di +
-
-Dielectricsemsm.esm.di +Linear Dielectricsemsm.esm.ld
- -Linear Dielectricsemsm.esm.di.ld +Susceptibility, Permittivity, Dielectric Constantemsm.esm.ld.sp + + +
- +Boundary Value Problems with Linear Dielectricsemsm.esm.ld.bvp + + +
- +Energy in Dielectric Systemsemsm.esm.ld.e + + +
- +Forces on Dielectricsemsm.esm.ld.f @@ -1661,7 +1690,7 @@ so we get Substituting this in \ref{Gr(8.6)} and using the divergence theorem, we obtain -
- -Polarizationemsm.esm.p - - -
- -Dielectricsemsm.esm.di - - -
-
+
-The Field of a Polarized Objectemsm.esm.fpo +Matter Bathed in E Fields; Polarizationemsm.esm.mE
- -Physical Interpretation of Bound Chargesemsm.esm.fpo.pibc +Overviewemsm.esm.mE.o
- -The Field Inside a Dielectricemsm.esm.fpo.fid +Polarizationemsm.esm.mE.P + + + +
+ -
+
+++
+Polarized Objects; Bound Chargesemsm.esm.po + + +
+-
+
- +Physical Interpretation of Bound Chargesemsm.esm.po.pibc + + +
- +The Field Inside a Dielectricemsm.esm.po.fid @@ -750,18 +763,34 @@ Table of contents
+ - +Dielectricsemsm.esm.di +
-
-Dielectricsemsm.esm.di +Linear Dielectricsemsm.esm.ld
- -Linear Dielectricsemsm.esm.di.ld +Susceptibility, Permittivity, Dielectric Constantemsm.esm.ld.sp + + +
- +Boundary Value Problems with Linear Dielectricsemsm.esm.ld.bvp + + +
- +Energy in Dielectric Systemsemsm.esm.ld.e + + +
- +Forces on Dielectricsemsm.esm.ld.f @@ -1593,8 +1622,8 @@ Table of contents emd.emw
- -Polarizationemsm.esm.p - - -
- -Dielectricsemsm.esm.di - - -
-
+
-The Field of a Polarized Objectemsm.esm.fpo +Matter Bathed in E Fields; Polarizationemsm.esm.mE
- -Physical Interpretation of Bound Chargesemsm.esm.fpo.pibc +Overviewemsm.esm.mE.o
- -The Field Inside a Dielectricemsm.esm.fpo.fid +Polarizationemsm.esm.mE.P + + + +
+ -
+
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+Polarized Objects; Bound Chargesemsm.esm.po + + +
+-
+
- +Physical Interpretation of Bound Chargesemsm.esm.po.pibc + + +
- +The Field Inside a Dielectricemsm.esm.po.fid @@ -750,18 +763,34 @@ Table of contents
+ - +Dielectricsemsm.esm.di +
-
-Dielectricsemsm.esm.di +Linear Dielectricsemsm.esm.ld
- -Linear Dielectricsemsm.esm.di.ld +Susceptibility, Permittivity, Dielectric Constantemsm.esm.ld.sp + + +
- +Boundary Value Problems with Linear Dielectricsemsm.esm.ld.bvp + + +
- +Energy in Dielectric Systemsemsm.esm.ld.e + + +
- +Forces on Dielectricsemsm.esm.ld.f @@ -1623,7 +1652,7 @@ so for a monochromatic EM plan wave, \] or more succinctly: -
- -Polarizationemsm.esm.p - - -
- -Dielectricsemsm.esm.di - - -
-
+
-The Field of a Polarized Objectemsm.esm.fpo +Matter Bathed in E Fields; Polarizationemsm.esm.mE
- -Physical Interpretation of Bound Chargesemsm.esm.fpo.pibc +Overviewemsm.esm.mE.o
- -The Field Inside a Dielectricemsm.esm.fpo.fid +Polarizationemsm.esm.mE.P + + + +
+ -
+
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+Polarized Objects; Bound Chargesemsm.esm.po + + +
+-
+
- +Physical Interpretation of Bound Chargesemsm.esm.po.pibc + + +
- +The Field Inside a Dielectricemsm.esm.po.fid @@ -750,18 +763,34 @@ Table of contents
+ - +Dielectricsemsm.esm.di +
-
-Dielectricsemsm.esm.di +Linear Dielectricsemsm.esm.ld
- -Linear Dielectricsemsm.esm.di.ld +Susceptibility, Permittivity, Dielectric Constantemsm.esm.ld.sp + + +
- +Boundary Value Problems with Linear Dielectricsemsm.esm.ld.bvp + + +
- +Energy in Dielectric Systemsemsm.esm.ld.e + + +
- +Forces on Dielectricsemsm.esm.ld.f @@ -1624,7 +1653,7 @@ B_0 = \frac{k}{\omega} E_0 = \frac{1}{c} E_0. Generalizing to propagation in the direction of an arbitrary wavevector \({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the -
- -Polarizationemsm.esm.p - - -
- -Dielectricsemsm.esm.di - - -
-
+
-The Field of a Polarized Objectemsm.esm.fpo +Matter Bathed in E Fields; Polarizationemsm.esm.mE
- -Physical Interpretation of Bound Chargesemsm.esm.fpo.pibc +Overviewemsm.esm.mE.o
- -The Field Inside a Dielectricemsm.esm.fpo.fid +Polarizationemsm.esm.mE.P + + + +
+ -
+
+++
+Polarized Objects; Bound Chargesemsm.esm.po + + +
+-
+
- +Physical Interpretation of Bound Chargesemsm.esm.po.pibc + + +
- +The Field Inside a Dielectricemsm.esm.po.fid @@ -750,18 +763,34 @@ Table of contents
+ - +Dielectricsemsm.esm.di +
-
-Dielectricsemsm.esm.di +Linear Dielectricsemsm.esm.ld
- -Linear Dielectricsemsm.esm.di.ld +Susceptibility, Permittivity, Dielectric Constantemsm.esm.ld.sp + + +
- +Boundary Value Problems with Linear Dielectricsemsm.esm.ld.bvp + + +
- +Energy in Dielectric Systemsemsm.esm.ld.e + + +
- +Forces on Dielectricsemsm.esm.ld.f @@ -1621,7 +1650,7 @@ These take the form of coupled first-order partial differential equations for \( Since \({\boldsymbol \nabla} \cdot {\bf E} = 0\) and \({\boldsymbol \nabla} \cdot {\bf B} = 0\), we get the -
- -Polarizationemsm.esm.p - - -
- -Dielectricsemsm.esm.di - - -
-
+
-The Field of a Polarized Objectemsm.esm.fpo +Matter Bathed in E Fields; Polarizationemsm.esm.mE
- -Physical Interpretation of Bound Chargesemsm.esm.fpo.pibc +Overviewemsm.esm.mE.o
- -The Field Inside a Dielectricemsm.esm.fpo.fid +Polarizationemsm.esm.mE.P + + + +
+ -
+
+++
+Polarized Objects; Bound Chargesemsm.esm.po + + +
+-
+
- +Physical Interpretation of Bound Chargesemsm.esm.po.pibc + + +
- +The Field Inside a Dielectricemsm.esm.po.fid @@ -750,18 +763,34 @@ Table of contents
+ - +Dielectricsemsm.esm.di +
-
-Dielectricsemsm.esm.di +Linear Dielectricsemsm.esm.ld
- -Linear Dielectricsemsm.esm.di.ld +Susceptibility, Permittivity, Dielectric Constantemsm.esm.ld.sp + + +
- +Boundary Value Problems with Linear Dielectricsemsm.esm.ld.bvp + + +
- +Energy in Dielectric Systemsemsm.esm.ld.e + + +
- +Forces on Dielectricsemsm.esm.ld.f @@ -1617,7 +1646,7 @@ target="_blank">Creative Commons Attribution 4.0 International License.
- -Polarizationemsm.esm.p - - -
- -Dielectricsemsm.esm.di - - -
-
+
-The Field of a Polarized Objectemsm.esm.fpo +Matter Bathed in E Fields; Polarizationemsm.esm.mE
- -Physical Interpretation of Bound Chargesemsm.esm.fpo.pibc +Overviewemsm.esm.mE.o
- -The Field Inside a Dielectricemsm.esm.fpo.fid +Polarizationemsm.esm.mE.P + + + +
+ -
+
+++
+Polarized Objects; Bound Chargesemsm.esm.po + + +
+-
+
- +Physical Interpretation of Bound Chargesemsm.esm.po.pibc + + +
- +The Field Inside a Dielectricemsm.esm.po.fid @@ -750,18 +763,34 @@ Table of contents
+ - +Dielectricsemsm.esm.di +
-
-Dielectricsemsm.esm.di +Linear Dielectricsemsm.esm.ld
- -Linear Dielectricsemsm.esm.di.ld +Susceptibility, Permittivity, Dielectric Constantemsm.esm.ld.sp + + +
- +Boundary Value Problems with Linear Dielectricsemsm.esm.ld.bvp + + +
- +Energy in Dielectric Systemsemsm.esm.ld.e + + +
- +Forces on Dielectricsemsm.esm.ld.f @@ -1617,7 +1646,7 @@ target="_blank">Creative Commons Attribution 4.0 International License.
+{\bf Wave equations for electric and magnetic fields in vacuum} \[ @@ -1677,7 +1706,7 @@ target="_blank">Creative Commons Attribution 4.0 International License.
-diff --git a/build/emdm.html b/build/emdm.html index 4956e9e..d387e64 100644 --- a/build/emdm.html +++ b/build/emdm.html @@ -1,7 +1,7 @@ - +Created: 2022-02-21 Mon 10:33
+Created: 2022-02-21 Mon 20:41
Pre-Quantum Electrodynamics @@ -706,28 +706,41 @@ Table of contents-diff --git a/build/emdm_Me.html b/build/emdm_Me.html index 82a370b..4468f41 100644 --- a/build/emdm_Me.html +++ b/build/emdm_Me.html @@ -1,7 +1,7 @@ - +Created: 2022-02-21 Mon 10:33
+Created: 2022-02-21 Mon 20:41
Pre-Quantum Electrodynamics @@ -706,28 +706,41 @@ Table of contents - -Polarizationemsm.esm.p - - -
- -Dielectricsemsm.esm.di - - -
-
+
-The Field of a Polarized Objectemsm.esm.fpo +Matter Bathed in E Fields; Polarizationemsm.esm.mE
- -Physical Interpretation of Bound Chargesemsm.esm.fpo.pibc +Overviewemsm.esm.mE.o
- -The Field Inside a Dielectricemsm.esm.fpo.fid +Polarizationemsm.esm.mE.P + + + +
+ -
+
+++
+Polarized Objects; Bound Chargesemsm.esm.po + + +
+-
+
- +Physical Interpretation of Bound Chargesemsm.esm.po.pibc + + +
- +The Field Inside a Dielectricemsm.esm.po.fid @@ -750,18 +763,34 @@ Table of contents
+ - +Dielectricsemsm.esm.di +
-
-Dielectricsemsm.esm.di +Linear Dielectricsemsm.esm.ld
- -Linear Dielectricsemsm.esm.di.ld +Susceptibility, Permittivity, Dielectric Constantemsm.esm.ld.sp + + +
- +Boundary Value Problems with Linear Dielectricsemsm.esm.ld.bvp + + +
- +Energy in Dielectric Systemsemsm.esm.ld.e + + +
- +Forces on Dielectricsemsm.esm.ld.f @@ -1628,7 +1657,7 @@ dI = \frac{\partial \sigma_b}{\partial t} da_{\perp} = \frac{\partial P}{\partia \] We therefore have the -
+{\bf Polarization current density} \[ @@ -1646,7 +1675,7 @@ the polarization current is the result of linear motion of charge when polarization changes). We can check consistency with the continuity equation associated to the conservation of bound charges:
-
+{\bf E and B fields for a monochromatic EM plane wave} \[ @@ -1668,7 +1697,7 @@ target="_blank">Creative Commons Attribution 4.0 International License.
-diff --git a/build/emd_emw_we.html b/build/emd_emw_we.html index 177d261..18935fa 100644 --- a/build/emd_emw_we.html +++ b/build/emd_emw_we.html @@ -1,7 +1,7 @@ - +Created: 2022-02-21 Mon 10:33
+Created: 2022-02-21 Mon 20:41
Pre-Quantum Electrodynamics @@ -706,28 +706,41 @@ Table of contents-diff --git a/build/emdm_Me_Mem.html b/build/emdm_Me_Mem.html index 7f3f484..87647c0 100644 --- a/build/emdm_Me_Mem.html +++ b/build/emdm_Me_Mem.html @@ -1,7 +1,7 @@ - +Created: 2022-02-21 Mon 10:33
+Created: 2022-02-21 Mon 20:41
Pre-Quantum Electrodynamics @@ -706,28 +706,41 @@ Table of contents
+{\bf Poynting vector of a monochromatic EM wave} \[ @@ -1639,7 +1668,7 @@ This has a transparent physical interpretation: the energy density \(u\) flows w
Similary, we get the
-+{\bf Momentum density of a monochromatic EM wave} \[ @@ -1690,7 +1719,7 @@ target="_blank">Creative Commons Attribution 4.0 International License.
-diff --git a/build/emd_emw_mpw.html b/build/emd_emw_mpw.html index 51f16db..9803efd 100644 --- a/build/emd_emw_mpw.html +++ b/build/emd_emw_mpw.html @@ -1,7 +1,7 @@ - +Created: 2022-02-21 Mon 10:33
+Created: 2022-02-21 Mon 20:41
Pre-Quantum Electrodynamics @@ -706,28 +706,41 @@ Table of contents
--+
+-Prerequisites
-
@@ -1603,8 +1632,8 @@ Prerequisites
-+
+Objectives
-
@@ -1645,7 +1674,7 @@ target="_blank">Creative Commons Attribution 4.0 International License.
-diff --git a/build/emd_emw_ep.html b/build/emd_emw_ep.html index 2c05365..8b21f34 100644 --- a/build/emd_emw_ep.html +++ b/build/emd_emw_ep.html @@ -1,7 +1,7 @@ - +Created: 2022-02-21 Mon 10:33
+Created: 2022-02-21 Mon 20:41
Pre-Quantum Electrodynamics @@ -706,28 +706,41 @@ Table of contents
+{\bf Poynting's theorem} \[ @@ -1686,7 +1715,7 @@ energy is carried by EM fields out of \({\cal V}\) across its boundary surface.
Energy per unit time, per unit area carried by EM fields:
-+{\bf Poynting vector} \[ @@ -1699,7 +1728,7 @@ Energy per unit time, per unit area carried by EM fields:
We can thus express Poynting's theorem more compactly:
-+{\bf Poynting's theorem} \[ @@ -1712,7 +1741,7 @@ We can thus express Poynting's theorem more compactly:
where we have defined the total
-+{\bf Energy in electromagnetic fields} \[ @@ -1735,7 +1764,7 @@ Then, \] so we get the
-+{\bf Poynting theorem (differential form)} \[ @@ -1752,7 +1781,7 @@ and has a similar for to the continuity equation -
+\paragraph{Example 8.1} Current in a wire: Joule heating. Energy per unit time delivered to wire: from Poynting. Assuming that the field is uniform, the electric field parallel to the wire is @@ -1797,7 +1826,7 @@ target="_blank">Creative Commons Attribution 4.0 International License.
-diff --git a/build/emd_emw.html b/build/emd_emw.html index 52d85ec..420337f 100644 --- a/build/emd_emw.html +++ b/build/emd_emw.html @@ -1,7 +1,7 @@ - +Created: 2022-02-21 Mon 10:33
+Created: 2022-02-21 Mon 20:41
Pre-Quantum Electrodynamics @@ -706,28 +706,41 @@ Table of contents
This expression can be greatly simplified by introducing the
-+{\bf Maxwell stress tensor} \[ @@ -1672,7 +1701,7 @@ The element \(T_{ij}\) represents the force per unit area in the $i$th direction
We then obtain
-+{\bf EM force per unit volume} \[ @@ -1684,7 +1713,7 @@ We then obtain
where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
-+{\bf Total force on charges in volume} \[ @@ -1713,7 +1742,7 @@ target="_blank">Creative Commons Attribution 4.0 International License.
-diff --git a/build/emd_ce_poy.html b/build/emd_ce_poy.html index 01f82a7..ee19a9d 100644 --- a/build/emd_ce_poy.html +++ b/build/emd_ce_poy.html @@ -1,7 +1,7 @@ - +Created: 2022-02-21 Mon 10:33
+Created: 2022-02-21 Mon 20:41
Pre-Quantum Electrodynamics @@ -706,28 +706,41 @@ Table of contents
This is thus simply a conservation law for momentum, with
-+{\bf Momentum density in the EM fields} \[ @@ -1619,7 +1648,7 @@ This is thus simply a conservation law for momentum, with
In a region in which the mechanical momentum is not changing due to external influences, we then have the
-+{\bf Continuity equation for EM momentum} \[ @@ -1648,7 +1677,7 @@ target="_blank">Creative Commons Attribution 4.0 International License.
-diff --git a/build/emd_ce_mst.html b/build/emd_ce_mst.html index 732c909..f035020 100644 --- a/build/emd_ce_mst.html +++ b/build/emd_ce_mst.html @@ -1,7 +1,7 @@ - +Created: 2022-02-21 Mon 10:33
+Created: 2022-02-21 Mon 20:41
Pre-Quantum Electrodynamics @@ -706,28 +706,41 @@ Table of contents
+{\bf Continuity equation} \[ @@ -1655,7 +1684,7 @@ target="_blank">Creative Commons Attribution 4.0 International License.
-diff --git a/build/emd_ce_mom.html b/build/emd_ce_mom.html index 56f7902..ff7694a 100644 --- a/build/emd_ce_mom.html +++ b/build/emd_ce_mom.html @@ -1,7 +1,7 @@ - +Created: 2022-02-21 Mon 10:33
+Created: 2022-02-21 Mon 20:41
Pre-Quantum Electrodynamics @@ -706,28 +706,41 @@ Table of contents