- 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
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.