Q. A solid conducting sphere of radius 10cm is enclosed by a thin metallic shell of radius 20cm. A charge q=20μC is given to the inner sphere. Find the heat generated in the process when the inner sphere is connected to the shell by a conducting wire

(a) 12 J

(b) 9 J

(c) 24 J

(d) zero

Ans: (b)

Sol: Electric field , $\displaystyle E = \frac{kq}{r^2} $

Energy density = Energy per unit volume , $\displaystyle u = \frac{1}{2}\epsilon_0 E^2 $

Energy = Energy density × volume

Energy = $ \displaystyle \int _{10}^{20} \frac{1}{2}\epsilon_0 E^2 (4\pi r^2)dr $

= 9 J