A point charge is fixed at the origin of a rectangular coordinate system, and a second point charge is fixed at . The locus of all points in the xy plane with is a circle centred on the x axis. We have to find (a) the location of the centre of the circle and (b) the radius R of the circle.

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(a) and (b)

A point charge is fixed at the origin of a rectangular coordinate system, and a second point charge is fixed at . The locus of all points in the xy plane with is a circle centred on the x axis. Let the centre of the circle in the xy coordinate system be . Let the radius of the equipotential surface be R. We will measure all lengths in units of nm.

We will use the fact that the points A and B as shown in the diagram lie on the equipotential . Therefore, we have the conditions

or

or

Similarly, by using the condition that at B, we get

or

or

From equation (1) and (2), we find