A ring of radius a lies on the yz plane and has uniform positive charge Q. A small particle of mass m and charge -q is place in the center of the ring and constrained to move on the x-axis. (a) Show for x << a, the electric field is proportional to x. (b) Find the force on the particle as a function of x for x << a. (c) Show that if the particle has a small displacement
in +x, it will undergo simple harmonic motion. (d) What is the angular frequency w of this motion?