First slide

Pontial due to

Question

A conducting sphere of radius 10 cm is charged 10 μC. 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

Moderate

A

1 : 4
B

1 : 3
C

2 : 1
D

1 : 1

Solution

After redistribution, new charges on spheres are
$Q_{1}^{'} = (\frac{10}{10 + 20}) \times 10 = \frac{10}{3} μC and Q_{2}^{'} = (\frac{20}{10 + 20}) \times 10 = \frac{20}{3} μ C$
Ratio of charge densities, $\frac{σ_{1}}{σ_{2}} = \frac{Q_{1}^{'}}{Q_{2}^{'}} \times \frac{r_{2}^{2}}{r_{1}^{2}}$
$= \frac{10 / 3}{20 / 3} \times {(\frac{20}{10})}^{2} = \frac{2}{1} \{σ = \frac{Q}{4 {πr}^{2}}\}$

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