question_answer

Three identical metallic uncharged spheres A, B and C each of radius a, are kept at the corners of an equilateral triangle of side d(d>>a) as shown in Fig. The fourth sphere (of radius a), which has a charge q, touches A and is then removed to a position far away. B is earthed and then the earth connection is removed. C is then earthed. The charge on C is

A) \[\frac{qa}{2d}\left( \frac{2d-a}{2d} \right)\]

B) \[\frac{qa}{2d}\left( \frac{2d-a}{d} \right)\]

C) \[-\frac{qa}{2d}\left( \frac{d-a}{d} \right)\]

D) \[-\frac{2qa}{d}\left( \frac{d-a}{2d} \right)\]

Correct Answer: C

Solution :

[c] \[\frac{k{{q}_{1}}}{a}+\frac{kq}{2d}=0\] \[\text{or }{{q}_{1}}=\frac{-\,qa}{2d}\] \[\frac{k{{q}_{1}}}{a}+\frac{kq}{2d}+\frac{k{{q}_{1}}}{d}=0\] \[\text{or }{{q}_{2}}=\frac{-qa}{2d}\left( \frac{d-a}{d} \right)\]