Question

Two metal spheres of radii $ {{r}_{1}} $ and $ {{r}_{2}} $ are charged to the same potential. The ratio of the charge on the two spheres is

• A. 1
• B. $ \frac{1}{2} $
• C. $ {{r}_{1}}-{{r}_{2}} $
• D. $ {{r}_{1}}/{{r}_{2}} $

Answer 1

Answer: (D)

We know that the potential for a metal sphere
$ V=k\frac{q}{r} $
According to the question
$ {{V}_{1}}=k\frac{{{q}_{1}}}{{{r}_{1}}} $
and $ {{V}_{1}}=k\frac{{{q}_{2}}}{{{r}_{2}}} $
as $ {{V}_{1}}={{V}_{2}} $
$ k\frac{{{q}_{1}}}{{{r}_{1}}}=k\frac{{{q}_{2}}}{{{r}_{2}}} $
$ \frac{{{q}_{1}}}{{{r}_{2}}}=\frac{{{r}_{1}}}{{{r}_{2}}} $