Current density of discrete charges in 1D space

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SUMMARY

The discussion centers on calculating the electric field in a one-dimensional circular loop due to a positron-electron pair. The positron (e+) moves along the bottom hemisphere while the electron (e-) moves along the upper hemisphere, eventually annihilating at the rightmost position. The user applies Gauss' law to conclude that the electric field strength remains constant at arcs separated by the charges, where charge density is zero. The challenge lies in expressing the current density for the two charges in one-dimensional space using the electromagnetic (EM) field tensor.

PREREQUISITES
  • Understanding of Gauss' law in electromagnetism
  • Familiarity with the electromagnetic field tensor
  • Basic knowledge of charge density concepts
  • Concept of circular motion in a one-dimensional context
NEXT STEPS
  • Research the application of Gauss' law in non-traditional geometries
  • Study the formulation of current density in one-dimensional systems
  • Explore the properties and applications of the electromagnetic field tensor
  • Investigate the dynamics of particle motion in circular paths
USEFUL FOR

This discussion is beneficial for undergraduate physics students, particularly those studying electromagnetism, as well as educators seeking to clarify concepts related to electric fields and charge dynamics in non-standard geometries.

cedricyu803
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Hi guys I am new here.

I was asked by my professor a problem:

a positron-electron pair is produced at the leftmost position of a 1D circular loop of radius R. e+ moves along the bottom hemisphere and e- moves along the upper one. They are confined in the circular loop and perform circular motion, eventually annihilate at the rightmost position.

Now the question is to find the electric field in the loop at different polar angles (say the loop is centred at the origin). Note that the loop is ONE-dimensional.

I know immediately from Gauss' law that at each arc separated by the charges the E-field strength is constant because the charge density at except where the charges are is zero.

In order to find the VALUE of the E-field, I attempted to use the EM field tensor to solve the problem but I don't know how to express the current density due to the two charges in 1D space.

So can anyone give me some hint in solving the problem??
Please don't give me the detailed proof as I want to finish it myself.
BTW I m a year 1 undergrad and I have just read about EM field tensor, so I am not quite familiar with it.

Thanks a lot in advance
 
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Somebody, please help me. I have been thinking of this question without any progress
 

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