Question

A conducting sphere that carries a total charge of -6 micro-coulomb is placed at the center of a conducting spherical shell that carries a total charge of +1 micro-coulomb. The conductors are in elecctrostatic equilibrium. determine the charge on the OUTER SURFACE of the shell. (hint: sketch a field line diagram)

Answer 1

"Electrostatic equilibrium" means the charges are not moving around. There is zero E-field inside the conductors.

The -6uC charge of the conducting sphere resides entirely at its surface, evenly distributed.

Gauss' law and the equilibrium requirement tells you that there can be no net charge inside a conducting spherical surface that passes between the inner and outer surfaces of the outer shell. That means there must be +6uC on the inner surface.

In order to have a net charge of 1 uC, there must be a charge of -5uC on the outer surface of the conducting shell.