\begin{equation} \xi = - \frac{d \Phi_B}{dt} \qquad \textnormal{(Faraday's Law)} \end{equation}
An induced current or emf always opposes the change in flux.
\begin{equation} \xi = \oint \, (\vec{v} \times \vec{B}) \cdot d\vec{l} \end{equation} \begin{equation} \xi = v \, B \, l \end{equation}
\begin{equation} \oint \vec{E} \cdot d\vec{l} = \frac{d \Phi_B}{dt} \qquad \textnormal{(Induced electric field)} \end{equation}
\begin{equation} i_D = \epsilon \frac{d \Phi_E}{dt} \qquad \textnormal{(Displacement current)} \end{equation}
\begin{equation} \oint_S E \cdot dA = \frac{Q_{enc}}{\epsilon_0} \qquad \textnormal{(Gauss' law for E fields)} \end{equation} \begin{equation} \oint_S B \cdot dA = 0 \qquad \textnormal{(Gauss' law for B fields)} \end{equation} \begin{equation} \oint_{loop} E \cdot ds = - \frac{d \Phi_B}{dt} \qquad \textnormal{(Faraday's law)} \end{equation} \begin{equation} \oint_{loop} B \cdot ds = \mu_0 \textbf{i}_D + \frac{d \Phi_E}{dt} \qquad \textnormal{(Ampere's law with displacement current)} \end{equation}
\begin{equation} \xi_1 = -M \frac{di_2}{dt} \quad \xi_2 = -M \frac{di_1}{dt} \qquad \textnormal{(EMF with mutual inductance)} \end{equation} \begin{equation} M = \frac{N_2 \Phi_{B2}}{i_1} = \frac{N_1 \Phi_{B1}}{i_2} \qquad \textnormal{(Mutual inductance)} \end{equation}
\begin{equation} \xi = - \, L \frac{di}{dt} \qquad \textnormal{(Self inductance)} \end{equation} \begin{equation} L = \frac{N \, \Phi_B}{i} \end{equation}
\begin{equation} U = \frac{1}{2} L I^2 \qquad \textnormal{(Energy of inductor)} \end{equation} \begin{equation} u = \frac{B^2}{2 \, \mu_0} \qquad \textnormal{(In vacuum)} \end{equation} \begin{equation} u = \frac{B^2}{2 \, \mu} \qquad \textnormal{(Energy in material with magnetic permeability μ)} \end{equation}
\begin{equation} \tau = \frac{L}{R} \qquad \textnormal{(Time constant of R-L circuit)} \end{equation}
\begin{equation} \omega = \sqrt{ \frac{1}{LC}} \qquad \textnormal{(Frequency of electrical oscillations)} \end{equation}
\begin{equation} \omega' = \sqrt{ \frac{1}{LC} - \frac{R^2}{4L^2}} \qquad \textnormal{(Damping)} \end{equation}