Gen Phys 2

Electromagnetic waves

Relation between E and B

\begin{equation} E = c \, B \end{equation} \begin{equation} B = \epsilon_0 \, \mu_0 \, c E \end{equation} \begin{equation} c = \frac{1}{\sqrt{\epsilon_0 \, \mu_0}} \end{equation}

Describing EM waves

\begin{equation} \vec{E}(x,t) = \hat{j} E_{max} \textnormal{ cos } (kx - \zeta \, t) \end{equation} \begin{equation} \vec{B}(x,t) = \hat{k} B_{max} \textnormal{ cos } (kx - \zeta \, t) \end{equation} \begin{equation} E_{max} = c B_{max} \end{equation}

EM waves in matter

\begin{equation} v = \frac{1}{\sqrt{\epsilon \, \mu}} = \frac{1}{\sqrt{K \, K_m}} \frac{1}{\sqrt{\epsilon_0 \, \mu_0}} = \frac{c}{\sqrt{K \, K_m}} \end{equation}

Energy and momentum in EM waves

\begin{equation} \vec{S} = \frac{1}{\mu_0} \vec{E} \times \vec{B} \end{equation}

\begin{equation} Intensity = S_{avg} = \frac{E_{max} \, B_{max}}{2 \, \mu_0} = \frac{E_{max}^2}{2 \, \mu_0 \, c} \end{equation} \begin{equation} = \frac{1}{2} \sqrt{\frac{\epsilon_0}{\mu_0}} E_{max}^2 \end{equation} \begin{equation} = \frac{1}{2} \epsilon_0 \, c \, E_{max}^2 \end{equation} \begin{equation} \frac{1}{A} \frac{dp}{dt} = \frac{S}{c} = \frac{EB}{\mu_0 \, c} \qquad \textnormal{(Flow rate of EM momentum)} \end{equation}