Key Equations

Key Equations

Displacement current	$I_{\text{d}}={\epsilon }_0\frac{d{\text{Φ}}_{\text{E}}}{dt}$
Gauss’s law	${\displaystyle \oint \overrightarrow{E}·d\overrightarrow{A}}=\frac{Q_{\text{in}}}{{\epsilon }_0}$
Gauss’s law for magnetism	${\displaystyle \oint \overrightarrow{B}·d\overrightarrow{A}}=0$
Faraday’s law	${\displaystyle \oint \overrightarrow{E}·d\overrightarrow{l}}=-\frac{d{\text{Φ}}_{\text{m}}}{dt}$
Ampère-Maxwell law	${\displaystyle \oint \overrightarrow{B}·d\overrightarrow{l}}={\mu }_{0}I+{\epsilon }_0{\mu }_0\frac{d{\text{Φ}}_{\text{E}}}{dt}$
Wave equation for plane EM wave	$\frac{{\partial }^2{E}_y}{\partial x^2}={\epsilon }_0{\mu }_0\frac{{\partial }^2{E}_y}{\partial t^2}$
Speed of EM waves	$c=\frac{1}{\sqrt{{\epsilon }_0{\mu }_0}}$
Ratio of E field to B field in electromagnetic wave	$c=\frac{E}{B}$
Energy flux (Poynting) vector	$\overrightarrow{S}=\frac{1}{{\mu }_0}\overrightarrow{E}\times \overrightarrow{B}$
Average intensity of an electromagnetic wave	$I=S_{\text{avg}}=\frac{c{\epsilon }_0{E}_0^2}{2}=\frac{c{B}_0^2}{2{\mu }_0}=\frac{E_0{B}_0}{2{\mu }_0}$
Radiation pressure	$p=\{\begin{array}{cccc}I\text{/}c\hfill & & & \text{Perfect absorber}\hfill \\ 2I\text{/}c\hfill & & & \text{Perfect reflector}\hfill \end{array}$