Problem 16.

A solid metal sphere with radius 0.75 m carries a net charge of 0.13 nC. Find the magnitude of the electric field at the following locations:
a) at a point 0.15 m outside the surface of the sphere.
b) at a point outside the sphere, 0.1 m below the surface.

Solution

The specific property of conductor (metal) is that the electric field inside conductor (in equilibrium) is 0. From this property it is possible to obtain that the charge is distributed over the surface of conductor (not in the bulk).

In the present problem the conductor has the shape of sphere. It means that all the charge 0.13 nC will be on the surface of the sphere.

Then the electric field outside of the conductor is the same as the electric field of the point charge at the center of the sphere.

Then electric field inside of the conductor is 0.

(a) a point 0.15 m outside the surface of the sphere is at distance 0.15+0.75 = 0.9 m from the center of the sphere. Then electric field at this point is

(b) Electric field inside of the sphere (inside of the conductor) is 0.