Determine the force in z-direction on the gyrocenter of a charged particle

[Logarythmic]

Homework Statement

Determine the force in z-direction on the gyrocenter of a charged particle in a diverging magnetic field.

\frac{\partial B}{\partial z} < 0

Homework Equations

The Attempt at a Solution

Please give me a starter. Could I use the Lorentz force in this case?

 

[Astronuc]

Is there a discussion in one's text regarding magnetic force or magnetic pressure on a charged particle?

A short answer - the effective force on a charged particle in a spatially varying magnetic field is given by:

\vec{F}\,=\,-\mu_m\,\vec{\nabla}B

Hopefully one would be able to derive this relationship.

 

[Logarythmic]

I did it with the Lorentz Force on the guiding center and got the equation given by Astronuc but with a plus sign. I guess that the sign is dependent on the charge.