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Unformatted text preview: Chapter 20 Faraday’s Law and Maxwell’s Extension to Ampere’s Law 174 20 Faraday’s Law and Maxwell’s Extension to Ampere’s Law Consider the case of a charged particle that is moving in the vicinity of a moving bar magnet as depicted in the following diagram: When we view the situation from the reference frame of the magnet, what we see (as depicted just above) is a charged particle moving in a stationary magnetic field. We have already studied the fact that a magnetic field exerts a force B F h h h × = P v q on a charged particle moving in that magnetic field. Now let’s look at the same phenomenon from the point of view of the charged particle: Surely we aren’t going to change the force exerted on the charged particle by the magnetic field of the magnet just by looking at the situation from a different reference frame. In fact we’ve already addressed this issue. What I said was that it is the relative motion between the magnet and the charged particle that matters. Whether the charged particle is moving through magnetic field lines, or the magnetic field lines, due to their motion, are moving sideways through the particle, the particle experiences a force. Now here’s the new viewpoint on this situation : What we say is, that the moving magnetic field doesn’t really exert a force on the stationary charged v p B N S v B S N (where P v v h h − = ). Chapter 20 Faraday’s Law and Maxwell’s Extension to Ampere’s Law 175 particle, but rather, that by moving sideways through the point at which the particle is located, the magnetic field creates an electric field at that location, and it is the electric field that exerts the force on the charged particle. In this viewpoint, we have, at the location of the stationary charged particle, an electric field that is exerting a force on the particle, and a magnetic field that is exerting no force on the particle. At this stage it might seem that it would be necessary to designate the magnetic field as some special kind of magnetic field that doesn’t exert a force on a charged particle despite the relative velocity between the charged particle and the magnetic field. Instead, what we actually do is to characterize the magnetic field as being at rest relative to the charged particle. So, as viewed from the reference frame in which the magnet is at rest: the particle experiences a force F h directed out of the page in the diagram above due to its motion through the magnetic field. And, as viewed from the reference frame in which the charged particle is at rest: the particle finds itself in a stationary magnetic field but experiences the same force F h because it also finds itself in an electric field directed out of the page....
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