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Question
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)/(4pi ε_0 d)`
Where,
`ε_0` = Permittivity of free space
`1/(4pi ε_0) = 9 xx 10^9` N C−2 m−2
∴ `V = (6 xx 9 xx 10^9 xx 5 xx 10^-6)/0.1`
= 270 × 103
= 2.7 × 106 V
Therefore, the potential at the centre of the hexagon is 2.7 × 106 V.
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