E&M - flux encircled by orbit of particles is conserved

[Qyzren]

Prove that in a magnetic mirror the flux encircled by the orbit of the particles is conserved when the magnetic field varies.

How do you do this? i have no idea how to approach/start this!

 

[javierR]

The flux is BA for the circular orbits (as you change the direction of the B field, the orbits adjust direction so that the flux is clearly the same) where A=area for a circle, found from the radius R. You can relate the radius R to the value of the B-field (and other quantities). Rescale B to B'=aB everywhere in your equations and show that the flux is independent of "a".