An insulating solid sphere of radius a has a uniform charge density and carries a total positive charge Q.
a) Calculate the electric field as a function of radius r from the center of the sphere for r > a.
b) Calculate the electric field at a point inside the sphere as a function of radius r from the center of the sphere for r < a
c) Suppose an alpha particle is sent from infinity at 2.09∗10^9 cm/s towards the center of the sphere, and that Q is +100e. Under these conditions, for what value of a does the alpha particle reach the center of the sphere with zero kinetic energy?