# 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. - Physics

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

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=(6xxq)/(4piin_0d)

Where,

in_0= Permittivity of free space

1/(4piin_0)=9xx10^9 NC^-2 m^-2

therefore V=(6xx9xx10^9xx5xx10^-6)/0.1

=2.7xx10^6 V`

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

Concept: Potential Energy of a System of Charges
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#### APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 2 Electrostatic Potential and Capacitance
Q 2 | Page 87