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. $R_{1}^{2}/R_{2}^{2}$

Answer 1

Answer: (B)

${{R}_{2}}/{{R}_{1}}$

Answer 2

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