A regular hexagon of side (5 ~cm ) has a charge (10 C ) at each of its vertices. The potential at the centre of hexagon is

Step-by-step solution

Given, length of sides of hexagon, (r=5 ~cm =5 10⁻² ~m ) charge on each vertices of hexagon, (q=10 C ) (=10 10⁻⁶ C ) Now, according to the question, Due to one charge, potential on hexagon's centre (P ) is given as, potential, (V= 1 4 ₀ , q r ) Potential, (V= k q r ) ( [ k= 1 4 ₀ , k=9 10^9 C ^2 / N - m ^2 ] ) (V= 9 10^9 10⁻¹ 10⁻⁶ 5 10⁻² =9 2 10^3 10^2 ) (V=18 10^5 ~N - m ^2 / C ^2 ) Due to all six charges, total potential at the centre of hexagonal is (V_ total =6 (V₁ ) ) Now, from Eq. (i), we get (V_ lotal =6 18