A stationary ring of radius a lies in the yz plane and has a uniform positive charge Q. A small particle that has mass m and a negative charge -q is located at the center of the ring.
(a) Show that if x « a, the electric field along the axis of the ring is proportional to x. (Do this on paper. Your instructor may ask you to turn in this work.)
(b) Find the force on the particle as a function of x. (Use the following as necessary: k, q, m, a, Q, and x.)
(c) Show that if the particle is given a small displacement in the +x direction, it will perform simple harmonic motion. (Do this on paper. Your instructor may ask you to turn in this work.)
(d) What is the frequency of that motion? (Use the following as necessary: k, q, m, a, and Q.)