# Energy of the system of similar charges

We know that two same charges repel each other. To stop the charges from going away we have to exert an external force and hence energy is used. But if in a vacuum two similar charges are placed near each other then they will move away from each other to infinite distance. So the force due to each charge produces a displacement of infinity. Will the energy used by charge be infinity?

I think the assumption you are making is that the force acting on each particle is constant. But that isn't the case over here because when two charged particles of charge $$+q_1$$ and $$+q_2$$ respectively are separated by a distance $$r$$ the force of repulsion on each is given by: $$F(r)=\frac {k{q_1}{q_2}}{r^2}$$ Which as you can see obeys inverse square law. Now you might have noticed from this that the farther a particle is away the less is the force of repulsion and hence the work done it would tend to converge to a given value.
• When I said $W_{infinity}=0$ it implied that $\frac {k{q_1}{q_2}}{d}=C$, but you may notice that $r$ is tending to infinity and hence the LHS of the equation becomes 0 ,implying $C=0$ – Ramanujan_π Oct 20 at 18:12
• What is $W_{infinity}$?? – Shreyansh Oct 20 at 18:13