Prove that the field on the surface of a sphere carrying a uniformly distributed electric charge is equal to that which would have been established, if the entire charge were concentrated in the centre of the sphere.

Explanation

Construct a second sphere around the sphere under consideration and suppose it carries a charge equal in magnitude, but opposite in sign (Fig. 24.14). According to the result obtained in the previous problem, the charge of the outer sphere does not create a field inside it. Therefore the field between the spheres is created only by the charge of the internal sphere. If there is little difference between the radii of these spheres (i.c. if `R_(1)-R lt lt R)` , the field in between will be almost homogeneous, and its strength will be (see 37.5)
`E=(sigma)/(epsi_(0))=(Q)/(epsi_(0)S)=(Q)/(4pi epsi_(0)R^(2))`