Question

Question 2.2: 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.

Class 12 - Physics - Electrostatic Potential And Capacitance Electrostatic Potential And Capacitance Page-87

Answer 1

A regular hexagon ABCDEF of side 10cm has a charge 5 μC at each of its vertices as shown in figure.
Potential due to charge placed at A, at centre is Kq/r
Potential due to charge placed at B, at centre is Kq/r
...................
...........................
Potential due to Charge placed at F , at centre is Kq/r
so, total potential at centre of regular hexagon , V = V₁ + V₂ + V₃ + V₄ + V₅ + V₆
so, V = kq/r + kq/r + kq/r + kq/r + kq/r + Kq/r
V = 6kq/r
Hence, k = 9 × 10⁹Nm²/C² , q = 5 × 10⁻⁶C and r = 10cm = 0.1 m
Now, V = 6 × 9 × 10⁹ × 5 × 10⁻⁶/0.1 = 2.7 × 10⁶ Volts

Answer 2

Answer:

2.7 × 106 V.

Explanation:

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,

Where,

= Permittivity of free space

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