Question

A rectangular loop with a sliding connector of length $l$ is located in a uniform magnetic field perpendicular to the loop plane (Fig.). The magnetic induction is equal to $B$. The connector has an electric resistance $R$, the sides $AB$ and $CD$ have resistances $R_1$ and $R_2$ respectively. Neglecting the self-inductance of the loop, find the current flowing in the connector during its motion with a constant velocity $v$.

Answer 1

Motional emf $V=Bvl$
Net resistance of the circuit $=R+\frac{R_1{R}_2}{R_1+R_2}$
$\therefore$ Current through the connector, $i=\frac{Bvl}{R+\frac{R_1{R}_2}{R_1+R_2}}$