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Question

Four charges equal to -Q are placed at the four corners of a square and a charge q is at its centre.
If the system is in equilibrium, the value of 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
Q8(1+22)
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Solution

The correct option is B Q4(1+22)
Let the square is of side a.
Force |F1|=KQ2a2 where K=14πϵo
|F2|=KQ2(2a)2
|F3|=KQq(a2)2
As the system is in equilibrium, thus net force is equal to zero.
2KQ2a2+KQ2(2a)2=KQq(a2)2
q=Q4(1+22)

438435_41628_ans_6b91489252514c7dac6d9bca57109139.png

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