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If a conductor - a long rod - moves at constant speed across the "lines" of a uniform magnetic field, is there an EMF within this conductor? Or, if a conducting rod rotates at uniform rate, pivoted in the middle or at one of its ends in a uniform magnetic field perpendicular to the plane of rotation, is there an EMF generated within the conductor?

Dan
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DeSegnac
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3 Answers3

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If the setup you have in mind is like the image below, there will be a voltage across the conductor.

This is due to the fact that there no closed path for a current.

The mobile electrons in the conductor "feel" a magnetic force towards the b end of the rod.

The electrons "bunch" up at that end resulting in an electric field that points from a to b.

Assuming the velocity is constant, the force on the electrons due to the electric field cancels the magnetic force.

enter image description here

Alfred Centauri
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  • Fine description. But in your reasoning and formula WHERE IS THE CHANGE OF MAGNETIC FLUX IN TIME to, per Faraday, effect creation of the EMF? – DeSegnac Jul 16 '13 at 23:16
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    @DeSegnac, (1) stop yelling and (2) re-read the answer and see that the explanation for the voltage across the rod does not require Faraday's law. All that is needed is the Lorentz force law, – Alfred Centauri Jul 16 '13 at 23:25
  • @DeSegnac If you are looking for an explanation that directly applies Faraday's induction law, take a look at my comment under your question.(possible duplicate of...) – Mostafa Jul 16 '13 at 23:48
  • My sincere apologies for inducing your (1) for I never thought that emphasizing crucial idea in upper case would, to any one, mean yelling. I will change that for sure at least in any correspondence where you may be present. – DeSegnac Jul 16 '13 at 23:49
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    @DeSegnac All caps has meant shouting since the 1980s on the usenet. So does excessive use of bold. Use italics for most emphasis. – dmckee --- ex-moderator kitten Jul 16 '13 at 23:51
  • Thanks dmckee. It is a long time since the usenet and I am not that active in commenting on anything here or elsewhere. – DeSegnac Jul 17 '13 at 01:00
  • "This is due to the fact that there no closed path for a current." I do not understand why this is a necessary condition. – Farcher Jun 24 '17 at 06:16
  • @Farcher, a necessary condition for what? – Alfred Centauri Jun 24 '17 at 18:43
  • To me it reads that the second sentence states a condition for the production of the voltage mentioned in the first sentence? – Farcher Jun 24 '17 at 21:58
  • @Farcher, it's been a while since I wrote this answer so I'll just go with what I believe I was thinking at the time. If, for example, there were rails made of ideal conductor that the rod slides on and assuming an ideal and stationary 'shunt' rod across these rails somewhere, there would be a path for current through the moving rod. Then, there will be a current 'round the loop producing a magnetic field threading the loop that, combined with the external field, yields a constant magnetic flux through the surface bounded by the loop.... – Alfred Centauri Jun 25 '17 at 00:01
  • In that case, there would be no voltage across the bar. However, since there is no path for current, charge will be displaced by the Lorentz force until the electric force, due to the field from the displaced charge, precisely balances. – Alfred Centauri Jun 25 '17 at 00:03
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An EMF is generated whenever a conductor moves relative to a magnetic field so that the conductor is cutting across the magnetic field lines. The EMF generated is the cross product of the magnetic field and the motion of the conductor (I may have the sign flipped, don't remember off the top of my head).

To answer your rotating rod question: yes EMF is produced inside the rod. However, note that this EMF will not be end to end of the rod, but from each end to its center.

If you attached brushes to the ends of the rod such that they touched the inside of a fixed cylinder, then the whole apparatus would be a generator between this cylinder and the center of the rod. If you connected this generator to a load, current would now flow, which now produces a force on the rod, which would oppose its motion.

Dan
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Olin Lathrop
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  • In the "EMF is generated whenever a conductor moves relative to a magnetic field so that the conductor is cutting accross the magnetic field lines" there is no indication of a CHANGE OF THE MAGNETIC FLUX IN TIME in order to (by M. Faraday) generate EMF. Thus WHERE FROM the EMF? – DeSegnac Jul 16 '13 at 22:45
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Faraday's law relates to the amount of energy a charge would gain by going around a loop. This energy per unit charge is called an "EMF". Because there is no change in the flux through any surface in this situation, there is no loop that gives a charge a different energy.

This doesn't mean that there is no path that gives the particle a different energy. As Alfred Centauri's answer illustrates, a conductor moving through a magnetic field is subject to the Hall effect, which will create a voltage between the two ends. This is not a violation of faraday's law, because the closed-loop voltage remains zero.

Community
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Dan
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  • Thanks Dan. No loop no EMF! The Hall's effect involves an interaction between an electric current and magnetic field. In a (non-looped) conductor moving through a constant magnetic field there is no current - only a thermal or a random motion of "loose" electrons. Thanks Dan. Per A. Centauri someone could detect static electric field at the end of the conductor. Does anybody know of this kind of experiment? – DeSegnac Jul 17 '13 at 00:25