PHYS 126 | Work and Energy 3 - Non-uniform Magnetic Field
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- เผยแพร่เมื่อ 4 ต.ค. 2024
- The motion and energy of a particles as is moves in a non-uniform field.
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I understand the part where charge particle is made to spiral in a uniform B field. However, if a charge particle is made to spiral, it should radiate EM wave out according to Maxwell equations. So, there is EM energy radiating out from the charge and if energy is to be conserved, the spiraling has to come to a stop. Therefore, the uniform B field should in principle stop all spiraling motion of the charge particle by dissipating the orthogonal KE into radiating EM energy.
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Static B field can never do work on charge particle. Because in the example, the components of velocity may change but the net velocity remains constant thus the total kinetic energy is constant throughout so no work is really being done in the process.
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Pretty helpful, but the first part threw me off when the particle was drawn as circling across the B-field lines. Normally I see the guiding centre parallel to the B-field line whereas there is also the gyration around a singular B-field line. The part that's confusing further is how the kinematic and magnetic pressures are related. Sometimes I see the ratio, beta changing as the particle travels and other times it remaining constant. Anywho, one question is that although v_parallel is zero (being mirrored) and the v_perpendicular is at the max value. The question is when the particle is at the midplane, v_parallel is max. Here would we also consider the v_perpendicular to equal zero?
Hi, my notes say that in a non uniform B field, there will always be a force acting from a region of stronger B field to weaker B field. Does that mean that when a particle move from left to right, assuming left has a stronger B field, that it will speed up? Since the force is acting with it. But when it travels from weaker to stronger B field, the force is acting against it which will cause the particle to reverse direction?
can you do some math please
But the field doesn't accelerate the particle back or forth it just changes the direction the particle is going in. If it accelerated the particle in any direction it would be doing work on the charge and that isn't possible. Right?
Right. The B field applies a force to the particle, so it must change the particle's velocity, but it only changes the direction of velocity, not the magnitude.
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Thanks but not really.
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