Electrostatic Energy Loss?

Question

Consider a droplet with radius R and charge Q, and it breaks into two droplets with charges Q/2 and radius R'. They repel each other to a distance much greater than R'. What is the loss of electrostatic energy.

This problem really confuses me. My best understanding is the work to make the configuration of the smaller droplets is the engery loss. Yet, the seperation goes from zero to some distance d where d >> R'. I was just thinking what if a calculated the work it took to take one of these particles from infinity to a distance d from the other charge...

Is that the same amounto of energy?

Answer 1

When we consider this problem we do not consider the two drops to be seprated at all.The question of their separation can be handled by the interconversion of KE and PE and there no loss is involved. We require some energy to create a big drop at a point in bringing charges from infinity. We also require some energy to bring two smaller droplets of lesser radius but each having Q/2 charge at the same point from infinity. These two are not same hence we talk of loss of energy.

Answer 2

Yes, the work needed to make the configuration is the energy lost.