The figure shows a conducting sphere ' A ' of radius ' a ' which is surrounded by a neutral conducting spherical shell B of radius ' b ' ( a ). Initially switches S 1

Question

The figure shows a conducting sphere ' A ' of radius ' a ' which is surrounded by a neutral conducting spherical shell B of radius ' b ' ( > a ). Initially switches S 1 ​ , S 2 ​ and S 3 ​ are open and sphere ' A ' carries a charge Q . First the switch ' S 1 ​ ' is closed to connect the shell B with the ground and then opened. Now the switch ' S 2 ​ ' is closed so that the sphere ' A ' is grounded and then S 2 ​ is opened. Finally, the switch ' S 3 ​ ' is closed to connect the spheres together. Find the heat (in joule) which is produced after closing the switch S 3 ​ . [Consider b = 4 cm , a = 2 cm and Q = 80 μ C ]

TestHub · Accepted Answer

When outer surface is grounded charge ' $- Q$ ' resides on the inner surface of sphere ' $B$ ' Now sphere A is connected to earth potential on its surface becomes zero.

Let the charge on the surface A becomes q $\frac{kq}{a} - \frac{kQ}{b} = 0 \Rightarrow q = \frac{a}{b} Q$ Consider the figure. In this position energy stored $E_{1} = \frac{1}{8 π ε _{0} a} [\frac{a}{b} Q]^{2} + \frac{Q ^{2}}{8 π ε _{0} b} + \frac{1}{4 π ε _{0} b} [\frac{a}{b} Q] (- Q)$ when ' $S_{3}$ ' is closed, total charge will appear on the outer surface of shell ' B '. In this position energy stored $E_{2} = \frac{1}{8 π ε _{0} b} (\frac{a}{b} - 1)^{2} Q^{2}$ Heat produced $= E_{1} - E_{2} = \frac{Q ^{2} a ( b - a )}{8 π ε _{0} b ^{3}} = 180$

Physics - Electrostatics Question with Solution | TestHub

Doubts & Discussion

JEE Advanced (2028)