# Relativistic angular moment of electron in electric field

1. Jan 21, 2016

### Pentaquark5

1. The problem statement, all variables and given/known data
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 $v\ll 1$!
2. Relevant 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 $l^{ik}=x^i p^k-x^kp^i$
3. The attempt at a solution
I really don't know how to solve this problem, sorry!

2. Jan 25, 2016

### Simon Bridge

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?