# Effect of Charged Particles trapped in Magnetic Field on that Field

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?

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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.

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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?).