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Question

# Five point charges, each of value +q, are placed on five vertices of a regular hexagon of side L. The magnitude of the force on a point charge of value –q placed at the centre of the hexagon (in newton) is

A
Zero
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B
3q24πϵ0L2
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C
q24πϵ0L2
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D
q243πϵ0L2
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Solution

## The correct option is C q24πϵ0L2Suppose six charges were placed at the corners 1,2,3,4,5 and 6 of hexagon would have been zero. Rightarrow⇁F01+⇁F02+⇁F03+⇁F04+⇁F05+⇁F06=0 ⇒⇁F01+⇁F02+⇁F03+⇁F04+⇁F05=−⇁F06 ⇒∣∣∣Resultant of forces acting on chargeplaced at the centre O of hexagon∣∣∣=|⇁F06| ⇒|Resultant|=q24πϵ0r2; since r=L{∵sin 30∘=L2r} |Resultant|=q24πϵ0r2

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