Question

There are two uncharged identical metallic spheres 1 and 2 of radius r separated by a distance d (d > > r) .A charged metallic sphere of same radius having charge q is touched with one of the sphere. After sometime it is moved away from the system. Now the uncharged sphere is earthed. Charge on earthed sphere is :

• A. $+\frac{q}{2}$
• B. $-\frac{q}{2}$
• C. $-\frac{qr}{2d}$
• D. $-\frac{qd}{2r}$

Answer 1

Answer: (C)

$-\frac{qr}{2d}$

When the charged metallic sphere is touched with uncharged sphere of same radius, both the spheres acquire same potential. Hence the charge $q$ is equally distributed among the two spheres, and thus the uncharged sphere has $q/2$ charge.

Now the other sphere is earthed, hence its potential is zero.

Potential at its center due to sphere of charge $\frac{q}{2}$ at a distance of $d$ $=\frac{kq/2}{d}$

Let the charge on earthed sphere be $Q$.

Potential at its center due to its own charge $=\frac{kQ}{r}$.

$⟹\frac{kq/2}{d}+\frac{kQ}{r}=0$

$⟹Q=-\frac{qr}{2d}$