Show that if at some part of a field the lines of force have the from of concentric circles whose centres are at point O (as given in Fig. 3.39), the field intensity at each point in this part of the field should be inversely proportional to the distance from the point O.
.

Explanation

For closed path, net work is zero.
`W_(AB) + W_(BC) + W_(CD) + W_(DA) = 0`
`E_1 r_1 theta + 0 - E_2 r_2 theta + 0 = 0`
or `E_1 r_1 = E_2 r_2` or `E prop (1)/( r)`.
.