Gauss' law in one-dimensional space

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SUMMARY

Gauss' law is not applicable in one-dimensional space, as it requires a closed surface enclosing a volume. In the scenario presented, with a one-dimensional closed loop containing both positive and negative charges, the electric field must be determined using the principle of superposition. Each charge contributes to the electric field at any point in the loop, and the net electric field is the vector sum of the fields due to each charge. This approach is essential for accurately analyzing electric fields in lower dimensions.

PREREQUISITES
  • Understanding of Gauss' law and its limitations
  • Knowledge of electric field concepts
  • Familiarity with the principle of superposition
  • Basic physics principles related to charge interactions
NEXT STEPS
  • Study the principle of superposition in electrostatics
  • Explore electric field calculations for point charges
  • Review the limitations of Gauss' law in various dimensions
  • Investigate one-dimensional charge distributions and their effects
USEFUL FOR

Physics undergraduates, educators, and anyone interested in understanding electric fields and the application of Gauss' law in different dimensional contexts.

cedricyu803
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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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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,
 

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