# Can Gauss' Law be used to calculate the electric field generated by a uniformly charged thread?

• I

## Main Question or Discussion Point

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?

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ZapperZ
Staff Emeritus
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 and Dale 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

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