Q: Two concentric thin metallic spheres of radii R_{1} and R_{2} (R_{1} >R_{2} ) bear charges Q_{1} and Q_{2} respectively. Then the potential at r between R_{1} and R_{2} will be 1/(4πε_{0} ) times

(a) $\large \frac{Q_1 + Q_2}{r} $

(b) $\large \frac{Q_1}{R_1}+ \frac{Q_2}{r} $

(c) $\large \frac{Q_1}{R_1}+ \frac{Q_2}{R_2} $

(d) $\large \frac{Q_2}{R_1}+ \frac{Q_1}{R_2} $

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Ans: (b)

Sol: Let P be the point & O be the centre of concentric spheres , OP = r (say)

Potential at P = Potential at P due to Q_{1} + Potential at P due to Q_{2}

$\large V = \frac{1}{4\pi \epsilon_0} \frac{Q_1}{R_1} + \frac{1}{4\pi \epsilon_0} \frac{Q_2}{r} $

$\large V = \frac{1}{4\pi \epsilon_0} ( \frac{Q_1}{R_1} + \frac{Q_2}{r}) $