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Numerical

A regular hexagon of side 10 cm has a charge 5 µC at each of its vertices. Calculate the potential at the centre of the hexagon.

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#### Solution

The given figure shows six equal amounts of charges, q, at the vertices of a regular hexagon.

Where,

Charge, q = 5 µC = 5 × 10^{−6} C

Side of the hexagon, l = AB = BC = CD = DE = EF = FA = 10 cm

Distance of each vertex from centre O, d = 10 cm

Electric potential at point O,

`"V" = (6 xx "q")/(4piin_0"d")`

Where,

`in_0` = Permittivity of free space

`1/(4piin_0) = 9 xx 10^9 "NC"^-2 "m"^-2`

∴ `"V" = (6 xx 9 xx 10^9 xx 5 xx 10^-6)/0.1`

= 2.7 × 10^{6} V

Therefore, the potential at the centre of the hexagon is 2.7 × 10^{6} V.

Concept: Potential Energy of a System of Charges

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