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Q.

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 figure. 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

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a

$- \frac{qa}{2 d} (\frac{d - a}{d})$

b

$\frac{qa}{2 d} (\frac{2 d - a}{2 d})$

c

$\frac{2 qa}{d} (\frac{d - a}{2 d})$

d

$\frac{qa}{2 d} (\frac{2 d - a}{d})$

answer is C.

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Detailed Solution

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$\frac{{kq}_{1}}{a} + \frac{kq}{2 d} = 0 or q_{1} = \frac{- qa}{2 d}$

$\frac{{kq}_{2}}{a} + \frac{kq}{2 d} + \frac{{kq}_{1}}{d} = 0 or q_{2} = \frac{- qa}{2 d} (\frac{d - a}{d})$

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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 figure. 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