The voltage ${\displaystyle {\mathcal {E}}}$ (in volts) induced in a wire of length ${\displaystyle l}$ (in meters) cutting a magnetic field of strength ${\displaystyle B}$ (in gauss) at the velocity ${\displaystyle v}$ (in m/s) is:
${\displaystyle {\mathcal {E}}=Bvl=-{\frac {d{\phi }}{d{t}}},}$
where ${\displaystyle d{\phi }/d{t}}$ is the rate of cutting of lines of magnetic flux in maxwell per second and the minus is inserted because of Lenz’s law (q.v.). In vector notation,
${\displaystyle {\mathcal {E}}=\int (\mathbf {v} \times \mathbf {B} )\cdot dl}$