1. Consider a ring of charge with radius R and uniform charge per unit length λ where > 0. A negative point charge -q with mass m is constrained to lie on the axis passing through the ring's symmetry axis. The point charge is located a very, very small distance from the center of the ring. Show that the point charge approximately undergoes simple harmonic motion and find the corresponding frequency. Hint: show that the force on the point charge is approximately very similar to Hooke's law. You'll need to first find the electric field of the ring along it's symmetry axis.

1. Consider a ring of charge with radius R and uniform charge per unit length λ where > 0. A negative point charge -q with mass m is constrained to lie on the axis passing through the ring's symmetry axis. The point charge is located a very, very small distance from the center of the ring. Show that the point charge approximately undergoes simple harmonic motion and find the corresponding frequency. Hint: show that the force on the point charge is approximately very similar to Hooke's law. You'll need to first find the electric field of the ring along it's symmetry axis.