Question

Charged sphere in a uniform electric field. Consider the problem of a charged conducting sphere in the uniform external electric field. This is equivalent to the example from the notes with the added charge on the sphere. Find the electric field in the space outside the sphere. Assume that the sphere has radius R and total charge Q. (a) Since there is no charge in the space outside the sphere, this is obviously the case of Laplacian in the azimuthally symmetric spherical system. Write the Laplacian, and using the separation of variables cast it in the form with separate angular and radial parts. (b) By imposing the physical boundary condition at infinity and at the surface of the sphere find possible values of the integration constants and write the solution for the potential. (c) Finally, calculate Ē = 2,Vêr +(V)/rêg and find the surface charge distribution on the sphere o = 60*E(R).

Answer 1