For a uniformly charged ring of radius R , determine the distance from its centre along the axis where the electric field achieves its maximum value.

Step-by-step solution

The electric field at a distance x from the centre of a uniformly charged ring of radius R and charge Q on its axis is given by E = kQx (R^2 + x^2)^ 3/2 For the electric field to be maximum, dE dx = 0 d dx [ x (R^2 + x^2)^ 3/2 ] = 0 (R^2 + x^2)^ 3/2 1 - x 3 2 (R^2 + x^2)^ 1/2 2x (R^2 + x^2)^3 = 0 (R^2 + x^2)^ 1/2 [R^2 + x^2 - 3x^2] = 0 R^2 - 2x^2 = 0 x = R 2