Question

Tthe Van de Graaff generator and sphere we have been assuming since the start that they are not polarizing each other. This is an approximation. In this question we will start to be able to assess how good this approximation is ?

(a) Use the approximation that the Van de Graaff generator and ball are uniformly charged spheres to find the E-field very close to the surface of the Van de Graaff generator, at the point where the +ve x-axis passes through the surface.

(b) Repeat (a) for the location where the -ve x-axis passes through the surface of the Van de Graaff generator.

(c) Sketch a very close blow-up view of a piece of the surface of the Van de Graaff generator. The view should be so close that the surface looks flat. Draw a Gaussian surface that is a small cube extending through the surface with half of it inside the Van de Graaff’s surface and half of it outside. One face of the cube is inside the Van de Graaff and parallel to its surface. Another face is outside and parallel to the surface. What is the electric flux through the inside face?

(d) If we locate our cube on the positive x-axis, what is the flux through its faces that are perpendicular to the surface of the sphere?

(e) Use your Gaussian surface from (c) to find the surface charge density at the surface of Van de Graaff right on the positive x-axis.

(f) Repeat (e) for the point on the Van de Graaff generator right on the negative x-axis.

(g) Comment on how good the approximation is that the Van de Graaff generator is unpolarized.

Note: please answer only (e) (f) (g)

Answer 1

Sce chqe demi Eo 6. unko R2 h 'ntiJe face 's the Cube

here He a be s 'm Rsilue α.aais os(d) - e, aed. and all