Charged particle in magnetic field: show p = qBr at relativistic speeds

[Enigma77]

When a particle with electric charge q moves with speed v in a plane perpendicular to a magnetic field B, there is a magnetic force at right angles to the motion with magnitude qvB, and the particle moves in a circle of radius r. This formula for the magnetic force is correct even if the speed is comparable to the speed of light. Show that p = qBr even if velocity is comparible to c. Remember that F does not equal m*a at very high speeds.

Ive been working trying to solve this problem for several hours so I think I need some help. I've been trying to use the momentum principle, p(final) = p(initial) + F*t. Can anyone offer some help or advice?

 

[Astronuc]

Why would one use "p(final) = p(initial) + F*t."

Think of angular momentum. If the charge does not radiate, nor collides with another particle, then it has constant angular momentum.

When a particle moves with a relativistic velocity, what correction is applied to the mass? What about the magnetic field?

Think about the formula for angular momentum.