A conducting sphere of radius 10 cm is charged to 10 μ C. Anothe

Question

A conducting sphere of radius 10 cm is charged to

10 μ C

. Another uncharged sphere of radius 20 cm is allowed to touch it for some time. After that if the spheres are separated then surface density of charges, on the spheres will be in the ratio of:

Options:

A . 1:3

B . 3:1

C . 2:1

D . 1:1

Answer: Option C
:
C
After redistribution, new charges on sphere are

Q_{1} = (\frac{10}{10 + 20}) \times 10 = \frac{10}{3} μ C

and

Q_{2} = (\frac{20}{10 + 20}) \times 10 = \frac{20}{3} μ C

Ratio of charge densities

\frac{σ_{1}}{σ_{2}} = \frac{Q_{1}}{Q_{2}} \times \frac{r_{2}^{2}}{r_{1}^{2}} = (\frac{\frac{10}{3}}{\frac{20}{3}}) \times {(\frac{20}{10})}^{2} = \frac{2}{1}

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