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Question

Four point charges, each –q are placed at the corners of a square and another charge Q is placed at its centre. If the system is in equilibrium, then Q is

A
q4[1+22]
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B
q4[1+22]
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C
q2[1+22]
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D
q2[1+22]
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Solution

The correct option is B q4[1+22]

Consider the equilibrium of charge on any corner, say that at A.
For equilibrium FBcos 45+FDcos 45+FC=FO
i.e., 14πϵ0
i.e., [q2a212+q2a212+q2(a2)2]=14πϵ0aQ(a22)2
i.e., q i.e, q[12+12+12]=Q(12)
i.e., |Q|=q4(1+22)

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