Houjun Liu

faraday's law

We have that:

The change in volts in a relationship to the magnetic flux.

\begin{equation} \epsilon = \oint \vec{E} \cdot \dd{\vec{l}} = - \dv{\Phi_{b}}{t} \end{equation}

where, \(\Phi_{b}\) is the magnetic flux, namely how much magnetic field is through a surface:

\begin{equation} \Phi_{b} = \int \vec{B} \cdot \dd{\vec{A}} \end{equation}

usually, this is just \(BA\).

Note! This tells us that the EMF (electric field per length) is just negative the change of magnetic flux.