All Problems

Electromagnetic Induction. Maxwells Equations

Problem 3.334

There are two stationary loops with mutual inductance L12.L_{12} . The current in one of the loops starts to be varied as I1=αtI_{1}=\alpha t where α\alpha is a constant, tt is time. Find the time dependence Iˉ2(t)\bar{I}_ {2}(t) of the current in the other loop whose inductance is L2L_{2} and resistance RR.

Reveal Answer
I2=αL12R(1etR/L2)I_{2}=\frac{\alpha L_{12}}{R}\left(1-\mathrm{e}^{-t R / L_{2}}\right)