OpenStax University Physics/E&M/Electromagnetic Waves

$ℰ\mathrm{\&}ℳ$ (Vol. 2):    5:Electric Charges and Fields    6:Gauss's Law    7:Electric Potential    8:Capacitance    9:Current and Resistance    10:Direct-Current Circuits    11:Magnetic Forces and Fields    12:Sources of Magnetic Fields    13:Electromagnetic Induction    14:Inductance    15:Alternating-Current Circuits    16:Electromagnetic Waves

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Chapter 16

Electromagnetic Waves

Displacement current $I_d={\epsilon }_0\frac{d{\mathrm{\Phi }}_E}{dt}$ where ${\mathrm{\Phi }}_E=\int \overrightarrow{E}\cdot d\overrightarrow{A}$ is the electric flux.

Maxwell's equations $\begin{array}{cccc}{\oint }_S\overrightarrow{E}\cdot \mathrm{d}\overrightarrow{A}& =\frac{1}{{ϵ}_0}{Q}_{in}& {\oint }_S\overrightarrow{B}\cdot \mathrm{d}\overrightarrow{A}& =0\\ {\oint }_C\overrightarrow{E}\cdot \mathrm{d}\overrightarrow{\ell }& =-{\int }_S\frac{\partial \overrightarrow{B}}{\partial t}\cdot \mathrm{d}\overrightarrow{A}& {\oint }_C\overrightarrow{B}\cdot \mathrm{d}\overrightarrow{\ell }& ={\mu }_{0}I+{ϵ}_0{\mu }_0\frac{\mathrm{d}{\mathrm{\Phi }}_E}{\mathrm{d}t}\end{array}$
See also http://ethw.org/w/index.php?title=Maxwell%27s_Equations&oldid=157445
▭ Plane EM wave equation $\frac{{\partial }^2{E}_y}{\partial x^2}={\epsilon }_0{\mu }_0\frac{{\partial }^2{E}_y}{\partial t^2}$ where $c=\frac{1}{\sqrt{{\epsilon }_0\mu }}$ is the speed of light
▭ The ratio of peak electric to magnetic field is $\frac{E_0}{B_0}=c$ and the Poynting vector $\overrightarrow{S}=\frac{1}{{\mu }_0}\overrightarrow{E}\times \overrightarrow{B}$ represents the energy flux
▭ Average intensity $I=S_{ave}=\frac{c{\epsilon }_0}{2}{E}_0^2=\frac{c}{2{\mu }_0}{B}_0^2=\frac{1}{2{\mu }_0}{E}_0{B}_0$
▭ Radiation pressure $p=I/c$ (perfect absorber) and $p=2I/c$ (perfect reflector).

For quiz at QB/d_cp2.16

Displacement current $I_d={\epsilon }_0\frac{d{\mathrm{\Phi }}_E}{dt}$ where ${\mathrm{\Phi }}_E=\int \overrightarrow{E}\cdot d\overrightarrow{A}$ is the electric flux.

Maxwell's equations: ${ϵ}_0{\mu }_0=1/c^2$
${\oint }_S\overrightarrow{E}\cdot \mathrm{d}\overrightarrow{A}=\frac{1}{{ϵ}_0}{Q}_{in}$
${\oint }_S\overrightarrow{B}\cdot \mathrm{d}\overrightarrow{A}=0$
${\oint }_C\overrightarrow{E}\cdot \mathrm{d}\overrightarrow{\ell }=-{\int }_S\frac{\partial \overrightarrow{B}}{\partial t}\cdot \mathrm{d}\overrightarrow{A}$
${\oint }_C\overrightarrow{B}\cdot \mathrm{d}\overrightarrow{\ell }={\mu }_{0}I+{ϵ}_0{\mu }_0\frac{\mathrm{d}{\mathrm{\Phi }}_E}{\mathrm{d}t}$

$\frac{{\partial }^2{E}_y}{\partial x^2}={\epsilon }_0{\mu }_0\frac{{\partial }^2{E}_y}{\partial t^2}$ and $\frac{E_0}{B_0}=c$

Poynting vector $\overrightarrow{S}=\frac{1}{{\mu }_0}\overrightarrow{E}\times \overrightarrow{B}$=energy flux

Average intensity $I=S_{ave}=\frac{c{\epsilon }_0}{2}{E}_0^2=\frac{c}{2{\mu }_0}{B}_0^2=\frac{1}{2{\mu }_0}{E}_0{B}_0$

Radiation pressure $p=I/c$ (perfect absorber) and $p=2I/c$ (perfect reflector).