- #1
Giuops
- 1
- 1
- Homework Statement
- Find the four-momentum of a charged particle in an external, constant electric and magnetic field.
- Relevant Equations
- dpμ/dτ=q*Fμν*uν
pμ=muμ
I have to find pμ(τ) of a particle of mass m and charge q with v(0) = (vx(0), vy(0), vz(0)) in a electric field E parallel to the y-axis and a magnetic field B parallel to z axis, both constant and uniform, with E = B.
Here follows what I have done (see pictures below):
I wrote 4 differential equations (using that E=B) and called qE/m = a. The last equation (z axis) is immediately solved.
To solve the others, I substituted equation (1) in (2) and (3), obtaining this:
... but I don't know how to solve these. How do I find the x and y components of the four momentum?
Thanks for the read.
Here follows what I have done (see pictures below):
I wrote 4 differential equations (using that E=B) and called qE/m = a. The last equation (z axis) is immediately solved.
To solve the others, I substituted equation (1) in (2) and (3), obtaining this:
... but I don't know how to solve these. How do I find the x and y components of the four momentum?
Thanks for the read.