The radii of two concentric metal spheres are a and b (b gt a). The outer sphere is charged with a charge q. If the inner sphere is connected to the earth, what will be its charge?

Explanation

Let the charge of the inner sphere be Q.
Given that the charge of outer sphere is q.

Radii of the inner and outer sphere are a and b respectively.
As the inner sphere is earthed, the potential is zero.
Thus the net potential is
`1/(4 pi epsilon_(0))Q/a + 1/(4 pi epsilon_(0))q/b = 0`
[ `:' 1/(4 pi epsilon_(0))` is constant, so it is not equal to zero.]
`:. Q/a = -q/b`
or, `Q = -q a/b`
Therefore, charge of the inner sphere is `-q a/b`.