Ncert Exercises & Solutions

Q 2.2) A regular hexagon of side 10 cm has a charge 5 µC at each of its vertices. Calculate the potential at the center of the hexagon.

The given figure shows six equal amounts of charges, q, at the vertices of a regular hexagon.

Where,
Charge,

q = 5 μ C = 5 \times 10^{- 6} C

$q = 5 μ C = 5 \times 10^{- 6} C$
Side of the hexagon,
1 = 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 π ε_{0}} \cdot \frac{6 \times q}{d}

$V = \frac{1}{4 π ε_{0}} \cdot \frac{6 \times q}{d}$
Where,
Where, E = Permitivity of free space and

\frac{1}{4 π ε_{0}} = 9 \times 10^{9} N m^{2} C^{- 2}

$\frac{1}{4 π ε_{0}} = 9 \times 10^{9} N m^{2} C^{- 2}$

$∴ V = \frac{9 \times 10^{9} \times 6 \times 5 \times 10^{- 6}}{0.1} = 2.7 \times 10^{6} V$
Therefore, the potential at the centre of the hexagon is 2.7 x

$10^{6}$ V.

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