# 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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## 2 Answers

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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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.

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Well it has been many years since I have taken a physics class (particularly E&M), and I recall both right hand rules. It seems to support my initial thought that the field would get successively stronger over time. This would be corollary to a stream of objects being trapped by the gravitational field of a larger object - the net field would increase over time. – nicholas Jun 23 '12 at 18:13
When I work through it, the induced magnetic field opposes the externally applied field. – Art Brown Jun 23 '12 at 18:55