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Question

# Five point charges, +q each, are placed at the five vertices of a regular hexagon. The distance of centre of the hexagon from any of the vertices is a. The electric field at the centre of the hexagon is

A
q4πϵ0a2
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B
q8πϵ0a2
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C
q16πϵ0a2
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D
Zero
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Solution

## The correct option is A q4πϵ0a2Suppose the charge is present at the sixth vertex also, then the electric field at centre would be zero. Now, if charge is not present at this vertex, the electric field at centre would be because of other five charges, which should be equal and opposite nature to the field produced due to a single charge at the sixth vertex. So the electric field at the centre of the hexagon is E=q4πϵ0a2 Hence, option (a) is the correct answer.

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