- #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.