{\bf Angular momentum of EM fields} \[ @@ -1638,7 +1642,7 @@ The angular momentum of EM fields is directly given by
diff --git a/build/emd_ce_ce.html b/build/emd_ce_ce.html index 1a46624..7079275 100644 --- a/build/emd_ce_ce.html +++ b/build/emd_ce_ce.html @@ -1,7 +1,7 @@ - +
- +Section and equation labellingin.t.l + + +
- Contextual colorsin.t.c @@ -736,7 +740,7 @@ Table of contents
- -Dielectricsemsm.esm.d +Dielectricsemsm.esm.di
-
@@ -1640,7 +1644,7 @@ This means that
\]
Since this is true for any volume, we have (re)derived the
-+
{\bf Continuity equation} \[ @@ -1668,7 +1672,7 @@ imposes a functional constraint on these sources: not {\it any} \(\rho\) and
diff --git a/build/emd_ce_mom.html b/build/emd_ce_mom.html index 4738e76..8882f02 100644 --- a/build/emd_ce_mom.html +++ b/build/emd_ce_mom.html @@ -1,7 +1,7 @@ - +Pre-Quantum Electrodynamics @@ -272,6 +272,10 @@ Table of contents- +Section and equation labellingin.t.l + + +
- Contextual colorsin.t.c @@ -736,7 +740,7 @@ Table of contents
- -Dielectricsemsm.esm.d +Dielectricsemsm.esm.di
-
@@ -1633,7 +1637,7 @@ in which the first integral can be interpreted as the momentum stored in the EM
This is thus simply a conservation law for momentum, with
-+{\bf Momentum density in the EM fields} \[ @@ -1645,7 +1649,7 @@ 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} \[ @@ -1661,7 +1665,7 @@ In a region in which the mechanical momentum is not changing due to external inf
diff --git a/build/emd_ce_mst.html b/build/emd_ce_mst.html index 3c38404..77114e9 100644 --- a/build/emd_ce_mst.html +++ b/build/emd_ce_mst.html @@ -1,7 +1,7 @@ - +Pre-Quantum Electrodynamics @@ -272,6 +272,10 @@ Table of contents- +Section and equation labellingin.t.l + + +
- Contextual colorsin.t.c @@ -736,7 +740,7 @@ Table of contents
- -Dielectricsemsm.esm.d +Dielectricsemsm.esm.di
-
@@ -1675,7 +1679,7 @@ and similarly for \({\boldsymbol B}\). We thus get
This expression can be greatly simplified by introducing the
-+{\bf Maxwell stress tensor} \[ @@ -1698,7 +1702,7 @@ The element \(T_{ij}\) represents the force per unit area in the $i$th direction
We then obtain
-+{\bf EM force per unit volume} \[ @@ -1710,7 +1714,7 @@ We then obtain
where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
-+{\bf Total force on charges in volume} \[ @@ -1726,7 +1730,7 @@ where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
diff --git a/build/emd_ce_poy.html b/build/emd_ce_poy.html index f3001bb..c49685f 100644 --- a/build/emd_ce_poy.html +++ b/build/emd_ce_poy.html @@ -1,7 +1,7 @@ - +Pre-Quantum Electrodynamics @@ -272,6 +272,10 @@ Table of contents- +Section and equation labellingin.t.l + + +
- Contextual colorsin.t.c @@ -736,7 +740,7 @@ Table of contents
- -Dielectricsemsm.esm.d +Dielectricsemsm.esm.di
-
@@ -1687,7 +1691,7 @@ so we get
Substituting this in \ref{Gr(8.6)} and using the divergence theorem,
we obtain
-+
{\bf Poynting's theorem} \[ @@ -1712,7 +1716,7 @@ 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} \[ @@ -1725,7 +1729,7 @@ Energy per unit time, per unit area carried by EM fields:
We can thus express Poynting's theorem more compactly:
-+{\bf Poynting's theorem} \[ @@ -1738,7 +1742,7 @@ We can thus express Poynting's theorem more compactly:
where we have defined the total
-+{\bf Energy in electromagnetic fields} \[ @@ -1761,7 +1765,7 @@ Then, \] so we get the
-+{\bf Poynting theorem (differential form)} \[ @@ -1778,7 +1782,7 @@ and has a similar for to the continuity equation -
+\paragraph{Example 8.1} Current in a wire: Joule heating. Energy per unit time delivered to wire: from Poynting. Assuming that the field is uniform, the electric field parallel to the wire is @@ -1810,7 +1814,7 @@ and the value is as expected.
diff --git a/build/emd_emw.html b/build/emd_emw.html index cbf0db6..153afa1 100644 --- a/build/emd_emw.html +++ b/build/emd_emw.html @@ -1,7 +1,7 @@ - +Pre-Quantum Electrodynamics @@ -272,6 +272,10 @@ Table of contents- +Section and equation labellingin.t.l + + +
- Contextual colorsin.t.c @@ -736,7 +740,7 @@ Table of contents
- -Dielectricsemsm.esm.d +Dielectricsemsm.esm.di
-
@@ -1619,8 +1623,8 @@ Table of contents
emd.emw
--
+
+-Prerequisites
-
@@ -1629,8 +1633,8 @@ Prerequisites
-+
+Objectives
-
@@ -1658,7 +1662,7 @@ Objectives
diff --git a/build/emd_emw_ep.html b/build/emd_emw_ep.html index 9800bf7..daa05ee 100644 --- a/build/emd_emw_ep.html +++ b/build/emd_emw_ep.html @@ -1,7 +1,7 @@ - +Pre-Quantum Electrodynamics @@ -272,6 +272,10 @@ Table of contents- +Section and equation labellingin.t.l + + +
- Contextual colorsin.t.c @@ -736,7 +740,7 @@ Table of contents
- -Dielectricsemsm.esm.d +Dielectricsemsm.esm.di
-
@@ -1649,7 +1653,7 @@ so for a monochromatic EM plan wave,
\]
or more succinctly:
-+
{\bf Poynting vector of a monochromatic EM wave} \[ @@ -1665,7 +1669,7 @@ This has a transparent physical interpretation: the energy density \(u\) flows w
Similary, we get the
-+{\bf Momentum density of a monochromatic EM wave} \[ @@ -1703,7 +1707,7 @@ The {\it radiation pressure} is the momentum transfer per unit area per unit of
diff --git a/build/emd_emw_mpw.html b/build/emd_emw_mpw.html index 05e00f9..66d80a3 100644 --- a/build/emd_emw_mpw.html +++ b/build/emd_emw_mpw.html @@ -1,7 +1,7 @@ - +Pre-Quantum Electrodynamics @@ -272,6 +272,10 @@ Table of contents- +Section and equation labellingin.t.l + + +
- Contextual colorsin.t.c @@ -736,7 +740,7 @@ Table of contents
- -Dielectricsemsm.esm.d +Dielectricsemsm.esm.di
-
@@ -1650,7 +1654,7 @@ 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
-+
{\bf E and B fields for a monochromatic EM plane wave} \[ @@ -1681,7 +1685,7 @@ or if you prefer explicit real parts (adding a possible phase shift \(\delta\)):
diff --git a/build/emd_emw_we.html b/build/emd_emw_we.html index 4b87c7f..83cf2fe 100644 --- a/build/emd_emw_we.html +++ b/build/emd_emw_we.html @@ -1,7 +1,7 @@ - +Pre-Quantum Electrodynamics @@ -272,6 +272,10 @@ Table of contents- +Section and equation labellingin.t.l + + +
- Contextual colorsin.t.c @@ -736,7 +740,7 @@ Table of contents
- -Dielectricsemsm.esm.d +Dielectricsemsm.esm.di
-
@@ -1647,7 +1651,7 @@ 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
-+
{\bf Wave equations for electric and magnetic fields in vacuum} \[ @@ -1690,7 +1694,7 @@ the actual electric and magnetic fields are given by the real part.
diff --git a/build/emdm.html b/build/emdm.html index 0aacaaf..0b6b77c 100644 --- a/build/emdm.html +++ b/build/emdm.html @@ -1,7 +1,7 @@ - +Pre-Quantum Electrodynamics @@ -272,6 +272,10 @@ Table of contents- +Section and equation labellingin.t.l + + +
- Contextual colorsin.t.c @@ -736,7 +740,7 @@ Table of contents
- -Dielectricsemsm.esm.d +Dielectricsemsm.esm.di
-
@@ -1630,7 +1634,7 @@ Table of contents
diff --git a/build/emdm_Me.html b/build/emdm_Me.html index 795b7e7..37b1302 100644 --- a/build/emdm_Me.html +++ b/build/emdm_Me.html @@ -1,7 +1,7 @@ - +Pre-Quantum Electrodynamics @@ -272,6 +272,10 @@ Table of contents- +Section and equation labellingin.t.l + + +
- Contextual colorsin.t.c @@ -736,7 +740,7 @@ Table of contents
- -Dielectricsemsm.esm.d +Dielectricsemsm.esm.di
-
@@ -1630,7 +1634,7 @@ Table of contents
diff --git a/build/emdm_Me_Mem.html b/build/emdm_Me_Mem.html index 419b7f0..c187471 100644 --- a/build/emdm_Me_Mem.html +++ b/build/emdm_Me_Mem.html @@ -1,7 +1,7 @@ - +Pre-Quantum Electrodynamics @@ -272,6 +272,10 @@ Table of contents- +Section and equation labellingin.t.l + + +
- Contextual colorsin.t.c @@ -736,7 +740,7 @@ Table of contents
- -Dielectricsemsm.esm.d +Dielectricsemsm.esm.di
-
@@ -1654,7 +1658,7 @@ dI = \frac{\partial \sigma_b}{\partial t} da_{\perp} = \frac{\partial P}{\partia
\]
We therefore have the
-+
{\bf Polarization current density} \[ @@ -1672,7 +1676,7 @@ 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:
-