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Question

# Five equal and similar charges are placed at the corners of a regular hexagon as shown in figure. What is the electric field and potential at the centre of the hexagon?

A
53πε0ql,54πε0ql2
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B

14πε0ql,54πε0ql2

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C

54πε0ql,14πε0ql2

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D

14πε0ql,14πε0ql2

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Solution

## The correct option is D 54πε0ql,14πε0ql2 Here the distances from centre O to each charge is r=l/2sin30=l. As the potential is a scalar quantity so the potential at O is V=14πϵ0[q/r+q/r+q/r+q/r+q/r]=54πϵ0l as r=l As the electric field is a vector quantity so field at O cancel each other due to the charges at opposite corner and only one charge will contribute the field. Thus, E=q4πϵ0r2=q4πϵ0l2

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