What will a current carrying wire do between charged plates?

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Offline Atomic-S

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Consider two large (compared to the space between them) parallel plates, oppositely charged electrically. A long straight wire of negligible resistance rests midway between them. The wire carries a current. We wish to investigate the force acting on the wire. The net charge of the wire  and the larger circuit of which it is presumably a part was zero to begin with, and presumably still is Therefore, the electrostatic force exerted on the wire is zero.  The magnetic force exerted on the wire is also zero because the magnetic field generated by its environment is zero.

Now let us suppose that the wire begins moving along its own axis. This would appear to change nothing of the previous analysis, so that the force on the wire is still zero.

However, now let us move to a reference frame that is moving along with the wire. The wire now appears stationary, the plates are now moving in the opposite direction. Because they are charged, this movement constitutes a current, which is opposite on each plate due to their opposite charge. The result is the generation of a magnetic field that sits between the plates and points  parallel to the plates and at right angles to the wire. What this gives us is a wire which sits at right angles to a magnetic field while carrying a current, which should therefore be deflected toward one of the plates. Is it? And if it is, how can that be reconciled with the conclusion from other reference frame in which it was concluded that there is no basis for a deflection? On the other hand, if the wire is not deflected, something must be counterbalancing the magnetic deflection that should be happening. The only thing that is available to do so is the electrostatic field, but for that to act, the wire must have a nonzero charge, which would imply that charge is not conserved, but depends on the frame of reference, which is also difficult to understand inasmuch as the number of electrons and protons in the wire, you would think, is the same in both cases.


Offline lightarrow

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A net charge, let's say positive, appears inside the wire between the plates, but a negative one appears in the part of the wire which is outside of the plates (if you want to move the wire, in the plates frame of ref., it have to close itself in a circuit).
Anyway, to solve this problem exactly, shouldn't be particularly easy  [:)]
« Last Edit: 08/09/2012 19:51:38 by lightarrow »