The figure shows a conducting disc rotating about its axis in a perpendicular magnetic field $B$. A resistor of resistance $R$ is connected between the center and the rim. Calculate the current in the resistor. Does it enter the disc or leave it at the center? Radius of the disc is $5.0 \mathrm{cm}$, angular speed $\mathrm{\omega }=10 \mathrm{rad}/\mathrm{s}, \mathrm{B}=0.40 \mathrm{T}$ and $\mathrm{R}=10 \mathrm{\Omega }$

A square wire frame with side $a$ and a straight conductor carrying a constant current $I$ are located in the same plane . The inductance and the resistance of the frame are equal to $L$ and $R$ respectively. The frame was turned through $180°$ about the axis $OO\text{'}$ separated from the current-carrying conductor by a distance $b$. Find the electric charge having flown through the frame.

A metal rod of mass $m$ can rotate about a horizontal axis $O$, sliding along a circular conductor of radius $a$. The arrangement is located in a uniform magnetic field of induction $B$, directed perpendicular to the ring plane. The axis and the ring are connected to an emf source, to form a circuit of resistance $R$. Neglecting the friction, circuit inductance and ring resistance, find the law according to which the source emf must vary, to make the rod rotate with a constant angular velocity $\omega$.