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# A regular hexagon of side 10 cm has a charge 5 muC at each of its vertices. Calculate the potential at the center of the hexagon.

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Solution :
The given figure shows six equal amount of charge, q, at the vertices of a regular hexagon. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/NCERT_PHY_V01_XII_C02_E01_002_S01.png" width="80%"> <br> Where, Charge q=5 `muc=5xx10^(-6) c` <br> Sid e of the hexagon , I=AB=BC=CD=DE =EF =FA =10 cm <br> Distance of each vertex from centre O, d= 1 cm <br> Electric potential at point O <br> `V=(6xxq)/(4piin_(0)d)` <br> Where, <br> `in_(0)`=permitivity of free space <br> `1/(4piin_(0))=(6xx9xx10^(9)xx5xx10^(-6))/0.1` <br> `=2.7xx10^(6)V` <br> Therefore, the potential at the centre of the hexagon is `2.7xx10^(6) V`.

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