A uniformly charged ring of radius d has total charge Q and is fixed in place. A point charge −q of mass m is placed at its center. Both Q and q are positive. As a result, if the point charge is given a small velocity along the ring's axis of symmetry, it will oscillate about the ring's center.
a. Find the period T of the oscillations.
For the rest of the problem, we will consider this situation in a reference frame where the ring is moving along its axis of symmetry with a constant speed v, which may be comparable to the speed of light c. In this frame, the ring and point charge have charge Q′ and q′, and the point charge still oscillates about the ring's center.
b. What is the period T′ of oscillation of the point charge in this frame?
c. When the charge is a small distance Δx from the center of the ring, find the restoring force in