Energy of an uniformly charged bar of length L

AI Thread Summary
Calculating the electric potential energy of a uniformly charged bar of length L and total charge Q is challenging due to the lack of symmetry compared to a uniformly charged sphere. The bar's zero radius leads to an infinite electric field, resulting in infinite energy calculations. In contrast, if the charge were distributed over the surface of a cylinder, the energy calculation would yield a finite result. This difference highlights the importance of charge distribution in determining electric potential energy. Understanding these distinctions is crucial for accurate energy computations in electrostatics.
DaTario
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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
 
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Because there is less symmetry in the bar case than in the sphere case.
 
Ok with respect to the simmetry, but how this argument relates to divergence in the computation of the energy's integral?

Thanks,

DaTario
 
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.
 
ok. good.

thanks

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
 
That's right.
 

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