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Question

# Four positive point charges (+q) are kept at the four corners of a square of side ′l′. The net electric field at the midpoint of any one side of the square is(Take 14πε0=K):

A
4Kql2
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B
16Kq55.l2
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C
8Kq5.l2
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D
Kql2
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Solution

## The correct option is B 16Kq5√5.l2The electric field due to the two charges on that particular edge will be cancelled by one another. The electric field due to one of the charge at other corner will be:E=Kqr2=Kql2+(l2)2=45Kql2. Each charge will have an electric field of this magnitude with an angle 2θ between them wheretanθ=12cosθ=1√1+tan2θ=2√5as 0<θ<π/2Hence, resultant electric field at this point is :ER=2Ecosθ=2(45Kql2)(2√5)=165√5Kql2

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