Two concentric spheres of radii r₁ and r₂carry charges q₁ and q₂ respectively. If the surface charge density ( $σ$ ) is the same for both spheres, the electric potential at the common centre will be

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$\frac{σ}{ε_{0}} (r_{1} + r_{2})$

$\frac{σ}{ε_{0}} . \frac{r_{1}}{r_{2}}$

$\frac{σ}{ε_{0}} (r_{1} - r_{2})$

$\frac{σ}{ε_{0}} . \frac{r_{2}}{r_{1}}$

answer is D.

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Detailed Solution

The electric potential at the common centre is

$V = \frac{q_{1}}{4 π ε_{0} r_{1}} + \frac{q_{2}}{4 π ε_{0} r_{2}} N o w, σ = \frac{q_{1}}{4 π {(r_{1})}^{2}} = \frac{q_{2}}{4 π {(r_{2})}^{2}} ∴ V = \frac{σ 4 π {(r_{1})}^{2}}{4 π ε_{0} r_{1}} + \frac{σ 4 π {(r_{2})}^{2}}{4 π ε_{0} r_{2}} = \frac{σ}{ε_{0}} (r_{1} + r_{2})$