Relativistic angular moment of electron in electric field

  • #1

Homework Statement


Consider an electron with spin ##\vec{S}## and magnetic moment ##\vec{\mu}=-\frac{e}{m}\vec{S}##. It is moving with the velocity ##\vec{v}(t)## relative to the inertial frame of reference ##I## through the electric field ##\vec{E}##. Calculate the angular momentum the electron experiences in its instantaneous rest frame ##I'##!
Compute the angular momentum with respect to ##I## under the condition ##v\ll 1##!

Homework Equations


Lorentz Force: ##F^i=q F^{ik}u_k=q\gamma(\vec{E}\cdot\vec{v}, \vec{E}+\vec{v}\times\vec{B})##

Where ##F_{ik}:=\partial_i A_k-\partial_k A_i## is the Faraday-Tensor

and ##F^{ik}=\eta^{im}\eta^{kn}F_{mn}##

The angular momentum tensor is given by ##l^{ik}=x^i p^k-x^kp^i##

The Attempt at a Solution


I really don't know how to solve this problem, sorry!
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,874
1,655
Welcome to PF;
Perhaps you need to reread your course notes so far ... and review your understanding of angular momentum?

How would you normally find angular momentum?
 

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