Force of interaction between two halves of a cylinder of charge.

[Lavabug]

Homework Statement

Find the force of interaction per unit length between the upper and bottom halves of a cylinder of uniform charge density rho.

Homework Equations

Solution should be $\rho^2R^3/3\epsilon_0$

The Attempt at a Solution

Frustrated cause I've solved this problem in the past and don't recall how to do it.

There's no analytic expression for the field of half a cylinder yes? How would I start to set the problem up? Would I have to find the interaction energy first then take its gradient?

 

[ideasrule]

There's no analytic expression for the field of half a cylinder yes? How would I start to set the problem up? Would I have to find the interaction energy first then take its gradient?

I think the problem is assuming that the separation between the two halves is 0. If not, it would have given you the separation, which it didn't. So the field is just the field inside an infinitely long cylinder.

 

[Lavabug]

I think the problem is assuming that the separation between the two halves is 0. If not, it would have given you the separation, which it didn't. So the field is just the field inside an infinitely long cylinder.

For the E field I just divided my expression for charge inside$\rho.r^2/R^2$ by the surface of a finite cylinder 2pi*rL. Doesn't get me anywhere near the answer.