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Question

# Five equal charges each of value q are placed at the corners of a regular pentagon of side a. What will be the electric field at O if the charge q at A is replaced by −q then?

A
2q4πε0r2 along OA
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B
2q4πε0r2 along OB
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C
4q4πε0r2 along OC
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D
zero
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Solution

## The correct option is A 2q4πε0r2 along OAIf all charge will be at the corner then there will not any electric field at the center, because of arrangement is symmetric about the center of the pentagon.But when one charge removes then equilibrium will disturb and the electric field will be generated toward that vacant corner, and its magnitude will be equal to the -q charge at a point. but, when another −q charge is kept at that point then →E−q=14πε0qr2 along OA.Hence net electric field at the centre→Enet=→E−q+→Efour charges=14πε0qr2+14πε0qr2→Enet=14πε02qr2 along OA.

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