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Question

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 :
156217_150005aa45ab41ef995093eee39b1f92.png

A
qa2d(2da2d)
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B
qa2d(2dad)
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C
qa2d(dad)
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D
2qad(da2d)
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Solution

The correct option is C qa2d(dad)
In the first case when A is in contact with D:
q1=q2

In the second case, when B is earthed:
kq1a+kq2d=0q1=qa2d
In the third case when C is earthed:
kq2a+kq2d+kq1d=0q2=qa2d(dad)

173724_156217_ans_92f39bf64b7a40a4a616fa6fc8239b25.png

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