Question

Two charged spherical conductors of radii $ {{R}_{1}} $ and $ {{R}_{2}} $ are connected by a wire. Then the ratio of surface charge densities of the spheres $ {{\sigma }_{1}}/{{\sigma }_{2}} $ is

• A. $ {{R}_{1}}/{{R}_{2}} $
• B. $ {{R}_{2}}/{{R}_{1}} $
• C. $ \sqrt{({{R}_{1}}/{{R}_{2}})} $
• D. $ R_{1}^{2}/R_{2}^{2} $
• E. $ R_{2}^{2}/R_{1}^{2} $

Answer 1

Answer: (B)

$ \frac{{{q}_{1}}}{{{q}_{2}}}=\frac{{{C}_{1}}}{{{C}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}} $
and $ \frac{{{q}_{1}}}{{{q}_{2}}}=\frac{4\pi R_{1}^{2}{{\sigma }_{1}}}{4\pi R_{2}^{2}{{\sigma }_{2}}} $
$ \frac{{{R}_{1}}}{{{R}_{2}}}=\frac{4\pi R_{1}^{2}{{\sigma }_{1}}}{4\pi R_{2}^{2}{{\sigma }_{2}}} $
$ \therefore $ $ \frac{{{\sigma }_{1}}}{{{\sigma }_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}} $