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Q.

Consider a system composed of two metallic spheres of radii r₁ and r₂ connected by a thin wire and switch S as shown in the figure. Initially, S is in open position and the spheres carry charges q₁ and q₂ , respectively. If the switch is closed, then potential of the system is

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a

$\frac{1}{4 {πε}_{0}} (\frac{q_{1}}{r_{1}} + \frac{q_{2}}{r_{2}})$

b

$\frac{1}{4 {πε}_{0}} \frac{q_{1} q_{2}}{r_{1} r_{2}}$

c

$\frac{1}{4 {πε}_{0}} (\frac{q_{1} + q_{2}}{r_{1} + r_{2}})$

d

$\frac{1}{4 {πε}_{0}} (\frac{q_{1} + q_{2}}{\sqrt{r_{1} r_{2}}})$

answer is B.

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Detailed Solution

$V = \frac{net charge}{net capacity} = \frac{q_{1} + q_{2}}{4 {πε}_{0} (r_{1} + r_{2})}$

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Consider a system composed of two metallic spheres of radii r1 and r2 connected by a thin wire and switch S as shown in the figure. Initially, S is in open position and the spheres carry charges q1 and q2 , respectively. If the switch is closed, then potential of the system is