Energy of an uniformly charged bar of length L

[DaTario]

Hi All

I would like to know why is it so difficult to calculate by integration the electric potential energy of an uniformily charged bar of length L and total charge Q. I have tried hard, thinking it would be as easy as the case of a uniformly charged sphere but my efforts failed.

Why these two systems are so different ?

Best Regards

DaTario

[DaleSpam]

Because there is less symmetry in the bar case than in the sphere case.

[DaTario]

Ok with respect to the simmetry, but how this argument relates to divergence in the computation of the energy's integral?

Thanks,

DaTario

[clem]

The radius of your line charge is zero. This means an infinite E field at the wire.
The energy calculation is infinite because of this. The energy of a point charge is also infinite. You need finite fields to get finite energies.

[DaTario]

ok. good.

thanks

DaTario

[DaTario]

Let me just provoke a little further. If my bar (or rod) of length L were a cylinder surface uniformly charged, then no infinite would appear in the energy calculation. Is it?

best regards,

DaTario

[clem]

That's right.