Effect of Charged Particles trapped in Magnetic Field on that Field

Question

Given a stream of moving charged particles that encounter a uniform magnetic field such that they are trapped in a circular orbit, what effect do these particles have on the net magnetic field over time? Would the magnetic field get stronger or weaker as the number of trapped particles increase?

Answer 1

They always reduce the field, and this is the law that magnetic fields induce currents that reduce their strength, a special case of LeChatelier's principle.

Answer 2

This question reads like a homework problem (and if so is probably well past its expiration date). One approach is as follows:

1. Use the $\mathbf{F}=q \mathbf{v x B}$ Lorentz force law to determine the orientation of the particles' circular orbits (i.e. if the external B-field is along the +z axis, are the orbits clockwise or counter-clockwise when viewed from above?).

2. Use the Biot-Savart law to determine the direction of the secondary magnetic field created by the particles' solenoidal current.

This prescription is in effect two successive applications of the right-hand rule.