A conducting sphere of radius $10\, cm$ is charged $10\,\mu \,C$. Another uncharged sphere of radius $20\, cm$ is allowed to touch it for some time. After that if the sphere are separated, then surface density of charges, on the spheres will be in the ratio of
A$1:4$
B$1:3$
C$2:1$
D$1:1$
AIIMS 2002, Medium
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C$2:1$
c (c) After redistribution new charges on spheres are $Q{'_1} = \left( {\frac{{10}}{{10 + 20}}} \right) \times 10 = \frac{{10}}{3}\,\mu C$
and $Q{'_2} = \left( {\frac{{20}}{{10 + 20}}} \right) \times 10 = \frac{{20}}{3}\,\mu C$
Ratio of charge densities $\frac{{{\sigma _1}}}{{{\sigma _2}}} = \frac{{Q'_1}}{{Q'_2}} \times \frac{{{r_2}^2}}{{{r_1}^2}}$
$ = \frac{{10/3}}{{20/3}} \times {\left( {\frac{{20}}{{10}}} \right)^2} = \frac{2}{1}$$\left\{ {\sigma = \frac{Q}{{4\pi {r^2}}}} \right\}$
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