At the origin, the electric field is directed along the positive x -axis. A small circle centred at the origin intersects the axes at points A , B , C , and D , which have coordinates (a, 0) , (0, a) , (-a, 0) , and (0, -a) respectively. Among the points located on the periphery of the circle, the electric potential is minimum at

Step-by-step solution

The relation between electric field E and electric potential V is given by dV = - E d r . This implies that the electric potential decreases in the direction of the electric field. Since the electric field at the origin is directed along the positive x -axis, the potential decreases as the x -coordinate increases. The points on the circle are A(a, 0) , B(0, a) , C(-a, 0) , and D(0, -a) . Among these points, point A has the maximum x -coordinate ( x = a ). Therefore, the electric potential is minimum at point A .