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Question

# Four particle each having a charge q, are placed on the four vertices of a regular pentagon. The distance of each corner from the centre is a. Find the electric field at the centre of the Pentagon.

A
q4πϵ0a2 Along OE
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B
q3πϵ0a2 Along OE
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C
Zero
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D
q5πϵ0a2 Along EO
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Solution

## The correct option is D q5πϵ0a2 Along EOCharge =qdistance of each corner from the centre =aIf there is a charge at 5th vertex of polygon.F1+F2+F3+F4+F5=0⟶(1)From the above equation there is no charge at 5th vertex so F5 should be eliminated from equation (1)F1+F2+F3+F4+F5=F5Net force at the center is −VeF5=15qπϵ0a2 along EO

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