Question

(a) Plot the electric field of a charged conducting solid sphere of radius R as a function of the radial distance r, 0 < r < 1, from the center.

(b) Plot the electric field of a uniformly charged nonconducting solid sphere of radius R as a function of the radial distance r, 0 < r < 1, from the center.

Answer 1

1)

The electric field of a point charge Q can be obtained by a straightforward application of Gauss' law. Considering a Gaussian surface in the form of a sphere at radius r, the electric field has the same magnitude at every point of the sphere and is directed outward. The electric flux is then just the electric field times the area of the sphere.

The electric field at radius r is then given by:

If another charge q is placed at r, it would experience a force

2)

The electric field of a sphere of uniform charge density and total charge charge Q can be obtained by applying Gauss' law. Considering a Gaussian surface in the form of a sphere at radius r > R, the electric field has the same magnitude at every point of the surface and is directed outward. The electric flux is then just the electric field times the area of the spherical surface.

The electric field outside the sphere (r > R)is seen to be identical to that of a point charge Q at the center of the sphere.

For a radius r < R, a Gaussian surface will enclose less than the total charge and the electric field will be less. Inside the sphere of charge, the field is given by: