A particle of (positive) charge Q is assumed to have a fixed position at P. A second particle of mass m and (negative) charge moves at a constant speed in a circle of radius , centred at P. We have to derive an expression for the work W that must be done by an external agent on the second particle in order to increase the radius of the circle of motion, centred at P, to .

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The centripetal force required for the particle of mass m to move in a circular orbit of radius r with speed v is

. This is provided by the Coulomb force of attraction between the charges and . It is

We have the equation

The energy of the particle moving in a circular orbit in the attractive Coulomb field will be

Therefore, the work done by an external agent required for increasing the radius of the circle of motion from to will be