How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 28.0 in diameter to produce an electric field of 1500 just outside the surface of the sphere?
1500 whats? Newtons per Coulomb?
Use Gauss' law.
The product of the area (pi D^2/6) and the E-field at the surface is equal to the total charge inside the sphere divided by the constant "epsilon-zero". Find that constant and compute the total charge. Divide that charge by the electron charge (e) to get the number of excess electrons.
It is not necessary that the electrons be distributed uniformly, as long as there is spherical symmetry.
The surface area of a sphere is, of course,
A = 4 pi R^2 = pi D^2,
NOT what I wrote.
I was thinking of the volume, and then got the exponent wrong.
Use the area in Gauss' Law.