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Electrostatic Potential And Capacitance

Question

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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.

Solution

Given,

C harge, q = 5 \times 10^{- 6} C S ide of hexagon, r = 10 cm = 0.1 m

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Potential at the centre of the hexagon is given by

V = \frac{1}{4 {πε}_{0}} [\frac{q}{r} + \frac{q}{r} + \frac{q}{r} + \frac{q}{r} + \frac{q}{r} + \frac{q}{r}] = 6 \times (\frac{1}{4 {πε}_{0}}) q / r

V = \frac{6 \times 9 \times 10^{9} \times 5 \times 10^{- 6}}{0.1} = 2.7 \times 10^{6} V .

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