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.

Answer 1

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, $v=\frac{1}{4πe_0}.\frac{6xq}{d}$

Where,

Where, = Permittivity of free space and $\frac{1}{4pi_0}$= 9 ×10-9 Nm2 c-2

$v=\frac{9x10^9x6x5x10^-6}{0.1}=2.7x10^6V$

Therefore, the potential at the centre of the hexagon is 2.7 × 106 V