Question

Describe the construction and working of a Van de Graff generator with the help of a labeled diagram.

Answer 1

Let us consider a large spherical shell of radius R. If we place a charge of magnitude Q on such a sphere, the charge will spread uniformly over the surface of the sphere. The electric field inside the sphere is zero, and that outside the sphere is due to the charge Q at the center of the sphere. So, the potential outside is that of a point charge; and inside it is constant. We, thus, have:

Potential inside conducting spherical shell of radius R carrying charge Q = constant and is as follows9

Let us place a small sphere at the center of the large one such that the radius of the smaller sphere is r and the charge over its surface is q. At the surface of the small sphere:10

At the large spherical shell of radius R:11

If we consider the total charges in the system, that is, q and Q, then the total potential energy due to the system of charges is:12