Answer to Question #251170 in Electricity and Magnetism for Ronan

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 field 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

Find the charge of the solid sphere of charged uniformly:

$$Q=4\pi\epsilon_0R^2E.$$

The number of electrons:

$$N=\frac Qe=\frac{4\pi\epsilon_0R^2E}{e}=12·10^9.$$

The field 10 cm from the center of the sphere:

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