Charged particle motion in a uniform magnetic field

• chrisbaird

chrisbaird

Consider that we have a macroscopic, electrically charged, point object tracing out a circular path in a uniform magnetic field in the usual way due to the Lorentz force. Now we very slowly raise the overall strength of the magnetic field (slow enough that on one orbit, the object sees the same field). Will the instantaneous speed of the object increase, or will its speed stay the same and its radius of orbit decrease? Consider everything is large enough and slow enough that we can ignore relativistic effects and the object does not radiate.

What do you think? Let me ask you two questions:

(1) Can the magnetic field ever increase the kinetic energy of the particle?
(2) Is there an electric field in the case you described?

Well, a larger magnetic field would exert a larger magnetic force on the particle, providing a larger acceleration. But the larger acceleration is in the radial direction of its circular motion, so the tangential velocity will remain unchanged, so the radius of orbit must decrease. On the other hand, in circular motion, the centripetal acceleration is proportional to the tangential velocity, so it would seem a higher acceleration would mean higher velocity.