Question

How many excess electrons must be added to a plastic solid sphere that has a diameter of 0.26 m to produce an electric à ƒ ƒ ¯ ¬ eld of 1030 N/C at the edge of the surface? Assuming the charge is uniform, what is the electric field at 10 cm from the center?

Answer 1

First, find the charge of this solid sphere of uniform charge:

$$Q=4\pi\epsilon_0R^2E=0.13^2=1.94·10^{-9}\text{ C},\\\space\\ N=\frac Qe=12·10^9.$$

The electric field at 10 cm from the center is

$$E_i=\frac{Qr}{4\pi\epsilon_0R^3}=794\text{ N/C}.$$