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

In summary, the conversation discusses the use of Gauss's Law to calculate the electric field generated by a uniformly charged finite thread. The conversation concludes that while Gauss's Law can be used for any type of charge distribution, it may not always have a simple analytical solution. In the case of a finite line charge, numerical solutions would be needed. The potential and electric field of a finite uniformly charged thread can be found using the Coulomb integral, but there is not enough symmetry to make Gauss's law useful.
  • #1
Guillem_dlc
184
15
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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  • #3
Guillem_dlc said:
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.
 
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  • #4
  • #5
ZapperZ said:
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
 
  • #6
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.
 

1. What is Gauss's Law and how does it relate to calculating the electric field of a charged thread?

Gauss's Law is a fundamental law in electromagnetism that relates the electric field to the distribution of electric charge. It states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space. In the case of a charged thread, Gauss's Law can be used to calculate the electric field at a point outside the thread by considering the total charge enclosed by a cylindrical surface surrounding the thread.

2. What is the formula for calculating electric field using Gauss's Law for a charged thread?

The formula for calculating the electric field using Gauss's Law for a charged thread is E = Q/(2πε₀r), where E is the electric field, Q is the total charge enclosed by the cylindrical surface, ε₀ is the permittivity of free space, and r is the distance from the thread to the point where the electric field is being calculated.

3. Can Gauss's Law be used to calculate the electric field inside a charged thread?

No, Gauss's Law can only be used to calculate the electric field outside a charged thread. This is because the electric field inside the thread is not constant and varies based on the distribution of charge within the thread.

4. How does the angle of the thread affect the calculation of electric field using Gauss's Law?

The angle of the thread does not affect the calculation of electric field using Gauss's Law. The electric field is only dependent on the total charge enclosed by the cylindrical surface and the distance from the thread to the point where the electric field is being calculated.

5. Is Gauss's Law applicable to all types of charged threads?

Yes, Gauss's Law is applicable to all types of charged threads, as long as the charge distribution is known. This includes both solid and hollow threads, as well as threads with varying charge densities. The key is to enclose the thread with a cylindrical surface and use the total enclosed charge in the calculation.

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