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## Homework Statement:

- A particle of positive charge Q is fixed at point P. A second particle of mass m and negative charge -q moves at constant speed in a circle of radius 1'10 centered at P. Derive an expression for the work W that must be done by an external agent on the second particle to increase the radius of the circle of motion to r2

## Relevant Equations:

- NA

This is the diagram in mind

Some of my assumptions like the particle q will be moving with some initial velocity V1 in the circle of radius of r1 and when it moves to the circle of radius r2 its velocity will be V2 ( > V1) since its potential energy is decreased.

The amount of work done by external agent is change in potential energy

Uf - Ui = W (Work done by external agent by definition).

The initial configuration is rotating in circle of radius r1.

The potential energy in this configuration is Ui = Q*q/(4*π*ε0*r1);

The kinetic energy is Ki = 0.5*m*V1^2;

Ei = Ui+Ki

The total energy in cfg2 is

Ef = Q*q/(4*π*ε0*r2) + 0.5*m*V2^2;

But there are so many unknowns, I am not sure how to calculate the work done. Please advise.