Two charged particle A and B repel each other by a force `k/r^2` where is a constant and r is th separation between them. The particle A is clamped to a fixed point in the lab and the particle B which has a mass m, is released from rest with asn initial separartion `r_0` form A. Find the change in the potential energyof hte wo particle system as the separation increases to a large value. What will be the speed o the particle b in this situation?

Explanation

The situation is shown in ure. Take A+B as the system. The only exterN/Al force acting on the system is that needed to hold A fixed. (you can imagine the experimetn being conducted in a gravity freee region or the particles may be kept and allowed to move on a smooth horizontal surface, so that teh normal force balaces the force of gravity). This force does no work on the system because it acts on teh charge A which does not move. Thus, the exterN/Al forces do no work and internl forces ae conservative. The total mechanical energy must, therefore, remain constant. There are two interN/Alforces `F_(AB)` acting on A and`F_(BA)` acting on B. The force `F_(AB)` does no work beause it acts on A which does not moe. The work done by `F_(BA)` as the particle B is taken away is,
`W=int vecF.vec(dr)=int^oo_r_0 k/r^2dr=k/r_0`............i

The change in the potential energy of the system is `U_f-U_i=-W=-k/r_0`
As the total mechanical energy of the system is
`K_f+U_f=K_i+U_i`
or `K_f=K_i-(U_f-U_i)`
or, `1/2mv^2=k/r_0`
`or, v=sqrt((2k)/(mr_0))`