A hollow, metallic, spherical shell has exterior radius 0.750 m, carries no net

Question

A hollow, metallic, spherical shell has exterior radius
0.750 m, carries no net charge, and is supported on an insulating
stand. The electric field everywhere just outside its
surface is 890 N/C radially toward the center of the sphere.
Explain what you can conclude about (a) the amount of
charge on the exterior surface of the sphere and the distribution
of this charge, (b) the amount of charge on the interior
surface of the sphere and its distribution, and (c) the
amount of charge inside the shell and its distribution.

Explanation / Answer

a.) The total charge can be treated as a point charge as if thesphere were compacted to a point (by gauss' law). The magnitude ofthe charge can be found by the electric field equation: E=kQ/R^2.So,

890=(9x10^9)Q/(.75)^2 => Q=5.56x10^-8 C.

This charge is distributed uniformly on the outer surface, as italways is on a conductor.

b.) The charge on the is equal to -Q, since the net charge is zero.It is also distributed uniformly.

c.) The charge on the inside is equal to Q, inducing the charge onthe inside of the shell, which in turn induces the charge on theoutside. We can't say exactly how it is distributed due to gauss'law, but we at least know it is symmetric since the field isuniform.

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