Using Gauss's Law to Calculate Electric Field of a Charged Thread

[Guillem_dlc]

Hello,

Can not Gauss's Law be used to calculate the electric field generated by a uniformly charged finite thread?

I suppose it is because I can not consider the electric field constant (always going to the same direction), and for this I would have to do it by parts (the lateral flow, and the flow of the cylinder caps) as if they were two independent geometric objects, which makes it not a closed surface. true?

 

[anorlunda]

Here is a link to the case you describe. It derives the answer.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elelin.html#c1

After reading that, let us know if you have more questions.

 

[ZapperZ]

Hello,

Can not Gauss's Law be used to calculate the electric field generated by a uniformly charged finite thread?

I suppose it is because I can not consider the electric field constant (always going to the same direction), and for this I would have to do it by parts (the lateral flow, and the flow of the cylinder caps) as if they were two independent geometric objects, which makes it not a closed surface. true?

I don't quite understand what "... uniformly charged finite thread ... " means. Do you mean a finite line charge?

Note that Gauss's law can be used to calculate ANY type of charge distribution. However, it doesn't mean that it is solvable analytically for those charge distribution. The ones we deal with in intro physics are the ones with high symmetry that allow for the calculation of the electric flux to be simple enough.

So yes, Gauss's law can be used to calculate the electric field (or electric field flux) for a finite line charge. But you will have to solve it numerically, since there isn't a simple analytical solution, except at very far away in the spherical cow regime.

Zz.

 

[Guillem_dlc]

Here is a link to the case you describe. It derives the answer.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elelin.html#c1

After reading that, let us know if you have more questions.

The thing is that it's not clear to me why I can not apply Gauss's Law. that's the Coulomb Law

Thanks

 

[Guillem_dlc]

I don't quite understand what "... uniformly charged finite thread ... " means. Do you mean a finite line charge?

Note that Gauss's law can be used to calculate ANY type of charge distribution. However, it doesn't mean that it is solvable analytically for those charge distribution. The ones we deal with in intro physics are the ones with high symmetry that allow for the calculation of the electric flux to be simple enough.

So yes, Gauss's law can be used to calculate the electric field (or electric field flux) for a finite line charge. But you will have to solve it numerically, since there isn't a simple analytical solution, except at very far away in the spherical cow regime.

Zz.

Thanks!

Guillem

 

[Meir Achuz]

The potential and electric field of a finite uniformly charged thread is readily found from the Coulomb integral.
There is not enough symmetry to make Gauss's law useful.