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Q.

Three identical metallic uncharged spheres A,B and C of radius a are kept on the corners of an equilateral triangle of side d(d>>a). A fourth sphere (radius a ) which has 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

Qa2da-dd

b

Qa2d2d-ad

c

2Qadd-a2d

d

Qa2d2d-a2d

answer is C.

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Detailed Solution

qA=Q2

When B is earthed :

VB=0     kqBa+k(Q/2)d=0   qB=-Qa2d

When C is earthed :

 kqca+k(Q/2)d-k(Qa/2d)d=0  qc=Qa2da-dd

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