Gauss' law in one-dimensional space

In summary, In order to determine the electric field in a 1-dimensional closed loop with a positive and a negative charge at rest, one needs to use superposition of the electric fields generated by each charge. Gauss's Law does not apply in this situation as it requires a volume enclosed by a closed surface. It is important to take into account the direction of the electric field due to each charge in order to accurately determine the total electric field in the loop.
  • #1
cedricyu803
20
0
Hello I am new here.

Here is the situation:

There is a 1-dimensional closed loop and this loop spans a one-dimensional space.

If there are a +ve and a -ve charge at rest on some points in the loop, what should be the electric field in the loop?

The only thing I can think of is Gauss' law. But I went into trouble because I don't know how to apply it in a 1-dim space.

BTW, Please don't give too detailed proof to me. I got to solve it by myself. I just hope anyone can give me some hint.

I am a physics undergrad.

Thanks in advance
 
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  • #2
Gauss's law does not apply in one-dimension or even two. You need a volume enclosed by a closed surface to apply Gauss's Law. From your description, it appears you have a line segment with two charges on it which requires superposition of the electric fields generated by each charge,
 

What is Gauss' law in one-dimensional space?

Gauss' law in one-dimensional space is a mathematical law that describes the relationship between the electric field and the charge distribution in a one-dimensional system. It states that the electric flux through a closed surface is equal to the total charge enclosed by that surface.

What is the significance of Gauss' law in one-dimensional space?

Gauss' law in one-dimensional space is significant because it allows us to calculate the electric field at a point in a one-dimensional system by knowing the charge distribution. This simplifies the calculation of electric fields and has applications in various areas of physics and engineering.

How is Gauss' law in one-dimensional space derived?

Gauss' law in one-dimensional space is derived from the more general Gauss' law, which applies to three-dimensional systems. By considering a one-dimensional system with a cylindrical surface, we can simplify the equations and derive the one-dimensional form of the law.

Can Gauss' law in one-dimensional space be applied to real-world situations?

Yes, Gauss' law in one-dimensional space can be applied to real-world situations, such as the electric field in a wire or a long charged rod. However, it is important to note that this law is a simplified version and may not accurately describe more complex systems.

What are the limitations of Gauss' law in one-dimensional space?

Gauss' law in one-dimensional space is limited to systems with a one-dimensional symmetry, such as a wire or a long charged rod. It cannot be applied to more complex systems with varying dimensions or non-uniform charge distributions. Additionally, it assumes that the electric field is constant along the one-dimensional surface, which may not always be the case in real-world scenarios.

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