Current density of discrete charges in 1D space

[cedricyu803]

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

 

[cedricyu803]

Somebody, please help me. I have been thinking of this question without any progress