Problem $3$

A positive point charge $Q,$ with mass $m,$ is immersec a negatively charged uniform sphere with radius $R,$ at a distance from its center.

The total charge in the spherical charge distribution is $-Q.$ Its mass is $Mm.$

a$)$ Calculate the force exerted by the distribution of negative charge on the positive charge.

b$)$ Under the effect of the force the positive charge starts oscillating around the center of the sphere, while the sphere remains still. Please explain why.

c$)$ Calculate the oscillation period.

d$)$ Calculate the kinetic energy of the system when the positive charge passes on the center of the negatively charged sphere.