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

$(a)\;+\large\frac{q}{2}\qquad(b)\;-\large\frac{q}{2}\qquad(c)\;-\large\frac{qr}{2d}\qquad(d)\;-\large\frac{qd}{2r}$

Answer : (c) $\;-\large\frac{qr}{2d}$
Explanation :
When a charged metallic sphere is touched with one of the sphere their densities will become same . Therefore charge on both the spheres becomes $\;\large\frac{q}{2}$
Now
After earthing the $\;1^{st}\;$ sphere let the charge on $\;1^{st}\;$ sphere becomes $\;q^{|}\;.$
Then
$\large\frac{k\;q^{|}}{r}+\large\frac{\large\frac{k\;q}{2}}{d}=0 \quad \; since\; \; d > > r$
$q^{|}=-\large\frac{q\;r}{2\;d}\;.$
answered Feb 19, 2014 by
edited Feb 20, 2014 by yamini.v