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Two metal spheres (radii r₁ and r₂ with r₁ < r₂) are very far apart but are connected by a thin wire. If their combined charge is Q, then what is their common potential.

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$\frac{1}{4 π \in_{0}} \frac{Q}{r_{1} + r_{2}}$

$\frac{- 1}{4 π \in_{0}} \frac{Q}{r_{1} r_{2}}$

$\frac{1}{4 π \in_{0}} \frac{Q}{r_{1} r_{2}}$

$\frac{1}{4 π \in_{0}} \frac{Q}{r_{1} - r_{2}}$

answer is A.

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Detailed Solution

$K \frac{q_{1}}{r_{1}} = \frac{K (Q - q_{1})}{r_{2}}$

$q_{1} = \frac{{Qr}_{1}}{r_{1} + r_{2}}$

$v_{1} = \frac{{Kq}_{1}}{r_{1}} = \frac{kQ}{r_{1} + r_{2}}$

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