Consider a metallic hollow sphere with its centre at point O. Point charge +Q is kept in the vicinity of the given sphere as shown in the figure. If the sphere is electrically neutral, then calculate the electric potential at point A due to induced charges on the sphere only.

Explanation

We must be aware of the fact that any metallic object acquires uniform potential in an electrostatic condition. Net potential at point O must be the same as the net potential at point A. It is easier to find potential at point O. The electric potential at point O due to induced charge is zero as the net amount of charge induced on the spherical shell is zero. Net potential at the centre becomes `(Q)/(4pi epsilon_(0)d)`.
Net potential at A is same as that at O.
On the other hand, net potential at point A can also be written as:
`V=(1)/(4pi epsilon_(0)) (Q)/(sqrt(d^(2)+R^(2)))+V_("induced")`
Equating the two values we get the following:
`(Q)/(4piepsilon_(0)d)=(1)/(4pi epsilon_(0)) (Q)/(sqrt(d^(2)+R^(2)))+V_("induced")`
`rArr V_("induced") = (Q)/(4pi epsilon_(0)d)-(1)/(4pi epsilon_(0)) (Q)/(sqrt(d^(2)+R^(2)))`
`rArr V_("induced")=(Q)/(4pi epsilon_(0)) [(1)/(d)-(1)/(sqrt(d^(2)+R^(2)))]`