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Two metallic spheres of radii 1 cm and 2 cm are given charges 10^-2 C and 5 x 10^-2 C respectively. If they are connected by a connecting wire, the final charge on the smaller sphere is

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a

$1 \times 10^{- 2} C$

b

$2 \times 10^{- 2} C$

c

$3 \times 10^{- 2} C$

d

$4 \times 10^{- 2} C$

answer is B.

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Detailed Solution

common potential $V = \frac{Total charge}{Total capacity}$
$∴ V = \frac{10^{- 2} + (5 \times 10^{- 2})}{4 {πε}_{0} [10^{- 2} + 2 \times 10^{- 2}]} = \frac{6 \times 10^{- 2}}{4 {πε}_{0} \times (3 \times 10^{- 2})} = \frac{2}{4 {πε}_{0}}$
Final charge on smaller sphere
$\begin{array}{l} = C_{1} V = [4 {πε}_{0} \times 10^{- 2}] \times \frac{2}{4 {πε}_{0}} \\ = 2 \times 10^{- 2} C \end{array}$

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