First slide

Electrostatic potential

Question

A sphere of 4cm radius is suspended in a hollow sphere of 6cm radius. The inner sphere is charged to potential 3 e.s.u. and the outer sphere is earthed. The charge on the inner sphere is

Easy

A

$54 e . s . u .$
B

$\frac{1}{4} e . s . u .$
C

$30 e . s . u .$
D

$36 e . s . u .$

Solution

Suppose charge on inner sphere is $+ Q$ as shown.
Potential on inner sphere
$V = V_{1} + V_{2} = \frac{k Q_{1}}{r_{1}} + \frac{k Q_{2}}{r_{2}} = \frac{(1) Q}{4} + \frac{(1) (- Q)}{6} (∵ k = 1, Q_{1} = Q, Q_{2} = - Q) \Rightarrow 3 = Q (\frac{1}{4} - \frac{1}{6}) \Rightarrow Q = 36 e . s . u .$

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