A regular hexagon of side 10; cm has a charge | vedclass

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Question

The given figure shows six equal amount of charges, $q$, at the vertices of a regular hexagon.

Where, Charge, $q=5\, \mu\, C=5 	imes 10^{-6} \,C$

Vedclass · Accepted Answer

$2.7 	imes 10^{6} \;V$

Vedclass · Answer

The given figure shows six equal amount of charges, $q$, at the vertices of a regular hexagon.

Where, Charge, $q=5\, \mu\, C=5 	imes 10^{-6} \,C$

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 $O$

$V=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{6 	imes q}{d}$

Where,

Where, $\varepsilon_{0}=$ Permittivity of free space and $\frac{1}{4 \pi \varepsilon_{0}}=9 	imes 10^{9}\, Nm ^{2} \,C ^{-2}$

$	herefore V=\frac{9 	imes 10^{9} 	imes 6 	imes 5 	imes 10^{-6}}{0.1}=2.7 	imes 10^{6}\, V$

Therefore, the potential at the centre of the hexagon is $2.7 	imes 10^{6} \;V$

A regular hexagon of side $10\; cm$ has a charge $5 \;\mu\, C$ at each of its vertices. Calculate the potential at the centre of the hexagon.

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