A circular disk of radius R and mass M carries n point charges (q), attached at regular intervals around its rim. At time t = 0 the disk lies in the xy plane, with its center at the origin, and is rotating about the z axis with angular velocity ω0, when it is released. The disk is immersed in a (time-independent) external magnetic field B(s, z) = k(−s Ŝ + 2z ẑ), where k is a constant.

(a) Find the position of the center if the ring, z(t), and its angular velocity, ω(t), as functions of time. (Ignore gravity.)

(b) Describe the motion, and check that the total (kinetic) energy—translational plus rotational—is constant, confirming that the magnetic force  does no work.