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 amount 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=(6xxq)/(4piin_0d)`

Where,

`in_0`= Permittivity of free space

`1/(4piin_0)=9xx10^9 NC^-2 m^-2

`therefore V=(6xx9xx10^9xx5xx10^-6)/0.1`

`=2.7xx10^6 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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