Energy of an uniformly charged bar of length L

The key difference between the bar and the sphere is the presence of an infinite E field in the bar case due to its zero radius, which leads to an infinite energy calculation. However, if the bar were a cylinder with a finite radius, this would not be an issue and the energy calculation would be finite. In summary, the difficulty in calculating the electric potential energy of a uniformly charged bar of length L and total charge Q is due to the presence of an infinite E field, which is not present in the case of a uniformly charged sphere.
  • #1
DaTario
1,039
35
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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  • #2
Because there is less symmetry in the bar case than in the sphere case.
 
  • #3
Ok with respect to the simmetry, but how this argument relates to divergence in the computation of the energy's integral?

Thanks,

DaTario
 
  • #4
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.
 
  • #5
ok. good.

thanks

DaTario
 
  • #6
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
 
  • #7
That's right.
 

1. What is the definition of energy for an uniformly charged bar of length L?

The energy of an uniformly charged bar of length L is the amount of work required to assemble the bar from infinitesimal point charges, with each point charge having a charge of dq, starting from a configuration where all the point charges are infinitely far apart and ending in the final configuration where the bar is formed.

2. How is the energy of an uniformly charged bar of length L calculated?

The energy of an uniformly charged bar of length L can be calculated using the formula E = (1/2) * k * q^2 * ln(L/a), where k is the Coulomb constant, q is the total charge of the bar, and a is the radius of the bar in meters.

3. Does the energy of an uniformly charged bar of length L change with the distance between charges?

No, the energy of an uniformly charged bar of length L does not change with the distance between charges. It only depends on the total charge and the length of the bar.

4. What is the significance of the energy of an uniformly charged bar of length L?

The energy of an uniformly charged bar of length L is a measure of the potential energy stored in the electric field of the bar. It is also important in understanding the behavior of charged particles near the bar, as the energy affects the movement and interactions of these particles.

5. How does the energy of an uniformly charged bar of length L change with the length of the bar?

The energy of an uniformly charged bar of length L increases with the length of the bar. This is because as the length of the bar increases, the number of point charges also increases, resulting in a higher potential energy stored in the electric field of the bar.

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