Felici's law

In physics, Felici's law allows one to calculate the net charge through a circuit configuration in which there is a current induced by a variable magnetic field, such a conductor coil immersed in a variable magnetic field. This law makes it possible to calculate net charge in a period using initial flux and final flux.

$q(t)={1 \over {\mathrm {R}}}[\Phi (0)-\Phi (t)]$

Demonstration

$q(t)=\int _{0}^{t}i(\tau )d\tau ={1 \over {\mathrm {R}}}\int _{0}^{t}{f_{{em}}}(\tau )d\tau ={1 \over {\mathrm {R}}}[\Phi (0)-\Phi (t)]$

When ${f_{{em}}}(t)=-{d\Phi (t) \over dt}$