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## Homework Statement

A heavy nuclei can be approximately considered as a spherical ball with uniform volume density = 4/3 * 10^ 25 C/m3. If a nuclei with total charge Q = 92e splits into 2 equal spherical piece and they fly away. What will be the total electric energy change during this fission?

What I think it's asking for is the difference in energy between the 1 sphere and 2 sphere states.

## Homework Equations

[itex]W=(1/2)\int \rho V \text{d$\tau $}[/itex]

## The Attempt at a Solution

My approach here (if I'm interpreting the problem correctly) would be to calculate the energy for one sphere with charge 92e and then calculate the energy for one sphere of a different radius with charge 92e (and then times by 2).

I'm having difficulty approaching how to calculate the energy for a sphere of charge:

dU = dq * V(dr)

[itex]U = \int dq V(dr)[/itex]

[itex]U = (1/4 \pi ε)\int dq * (dr/r)[/itex]

I'm having trouble with the limits of integration, I tried from Infinity to 0, split it into Infinity to R and then R to 0 but I got infinities in the answer. If someone could just point me along the right direction here for how to attack this problem I'd appreciate it, it seems easy I'm just doing something wrong or missing something.

Thanks!