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Work done by the Lorentz force?

  1. Jun 13, 2014 #1
    When a wire is placed in a magnetic field and current flows in that wire work is done on the wire and be calculated:

    1) W = Fd
    2) F = IL x B
    3) W = ( IL x B )x d

    Must there be any derivations beyond what is above?
    If everything is "given" or... measured via instruments.

    Then when the wire starts to move, motional EMF can be calculated:
    ε = -vBL

    Is this correct?
  2. jcsd
  3. Jun 13, 2014 #2


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    Gold Member

    Pure magnetic fields do no work. They always act perpendicularly to the induced displacement.

    Pure magnetic fields yield a force which is perpendicular to the velocity, as such, the instantaneous power is $$\vec{F}_B\cdot\vec{v}=0$$. No work is being done.
  4. Jun 13, 2014 #3
    Every motor text says otherwise. Mag fields do work on mag dipoles, not on discrete charges. In a motor, when the torque, T, spins the rotor through angle θ, the work done equals T*θ. This mag field produced the torque. I posted pics a couple years ago illustrating the Lorentz mag force component aligning in direction of torque.

    The mag field is spinning the rotor and doing the work. Refer to thread below:


  5. Jun 13, 2014 #4


    Staff: Mentor

    Pure magnetic fields do no work directly. Per Poynting's theorem the work done by an EM field is equal to E.j.

    However, since B fields contain energy and since that energy can easily be transferred to E fields and thence to matter, I don't think that it is wrong to say that they do work, as long as it is understood that the work is always "mediated" by E.j.
  6. Jun 13, 2014 #5


    Staff: Mentor

    Looks fine to me.
    Last edited: Jun 13, 2014
  7. Jun 13, 2014 #6
    You're saying that the energy in B gets transferred to E, then E does the work. We already went through this, please refer to my diagram. E*J is a scalar, it does not describe the torque times angular displacement. Lorentz force magnetic component Fm = q(uXB), is a vector acting tangential to rotor producing a torque, except when poles are aligned where Fm produces no torque. E*J is the total energy density inputted to the entire motor from the power supply.

    E*J includes the energy stored in the windings, dissipated as heat in the resistance, frictional losses, and motional energy. E*J is the whole kit and caboodle. But Fm x r is the torque vector T. The integral of T*θ is the work moving the rotor.

    Please view my diagram which I cannot re-attach since it was already posted some time ago and I will elaborate. The link in my previous post will bring it up. Thanks.
    Last edited: Jun 13, 2014
  8. Jun 13, 2014 #7
    I don't really care what field does work honestly, as long as I can calculate the force using such a method.
  9. Jun 13, 2014 #8
    Thanks for the rest for the help.
  10. Jun 14, 2014 #9


    Staff: Mentor

    Yes, the whole "kit and caboodle" including the work done on the rotor. All of it. With none left over for B to do, except indirectly through E.j.
  11. Jun 16, 2014 #10
    B does the work in spinning the rotor with torque. But as B imparts energy to the rotor, its energy is replenished by E*J. Think of an elaborate system of ropes and pulleys lifting an object. The robe tied to the object can be said to exert a force on said object lifting it, doing work. But the other end of the rope is being yanked on, so that source is doing work on the rope.

    It's all about where you draw the system boundary. E & B fields can do short term work, but they must have their energy replenished, which the power source does. Ultimately the source provides E*J to replenish all fields.

    B does local work just as a rope lifts an object. But there is another source pulling the rope. B all alone cannot do long term work, same with E. It is the power source that ultimately does the global work. But E & B provide a means of focusing the forces/torques/displacement so as to do the job correctly. Without B exerting force on the rotor mag dipole, E*J cannot spin the rotor.

    E*J is the whole kit & caboodle. B is just the rotor work in spinning. Ultimately B does the work, but loses energy as rotor gains it. E*J replaces this energy. Mag fields do indeed do work just as elec fields, but it I short term. Power source does the global long term work.

  12. Jun 16, 2014 #11


    Staff: Mentor

    Hmm, I think of it in the same context, but exactly backwards from what you are suggesting. I think of E.j as being the rope and B as being the thing pulling on the rope.

    The reason is that by Poynting's theorem the only term which does work on matter is E.j whereas energy can go from B to E in the other terms. So E, like the rope, is the only field "attached" to matter for doing work, where as B, like the thing pulling the rope, only does work by its influence on E.j.

    I think that your approach is inconsistent with Poynting's theorem, or at least requires substantial explanation to justify its consistency.

  13. Jun 17, 2014 #12
    I need justification! Really Dale! I've not only given equations and explanation, but drawn pics as well. Anyway, one more time. E*J is a scalar. Not a vector. In order to spin the rotor, a torque is needed. This torque times the angular displacement is work done on the rotor. See the pic I drew. The force vector providing this torque, F X r, is the magnetic component of Lorentz force, Fm= q(u X B). The E vector does not point the right way. The E field provides the Lorentz force, Fe, , that maintains the rotor loop current. This current supports the rotating mag field of the rotor, and this mag field interacts with that of the stator to generate torque.

    An induction motor is very transformer-like. The rotor amp-turns get balanced by the stator amp-turns. The stator gets its power from the input source, which provides all energy computed per Poynting E*J. But Poynting does not detail which forces appear where nor the direction. E*J is a scalar and one cannot ascertain direction of torque/rotation from Poynting.

    My pics detail the normal & tangential components of E, B, Fe, & Fm. Please review them, you will be surprised. They actually illustrate what is going on. Every machines text in the world says Fm does the work n relation to B. But B depends on I which relates to J as well as E. At the power input E*J describes all power processed by the machine. But the E at the input is not the E at the rotor. We must distinguish which E, which B, which I/J, etc.

    Enough for now. Please review my pics, and if you have a question re the pics, I will elaborate. Without pics, discussion is not productive. Best regards.

  14. Jun 17, 2014 #13


    Staff: Mentor

    Yes, you need justification. None of your equations or pictures show how your concept is compatible with Poynting's theorem.

    Excellent, work is also a scalar, not a vector.

    Nice, but not relevant. Neither torque nor force are work, they are both vectors not scalars, as you have pointed out. The question isn't what forces are acting, but what work is being done. EM fields do not do work on rotors, they do work on currents, and the amount of work done is given by E.j per Poynting's theorem.

    The question remains, how is your view of B doing work directly (i.e. the rope) compatible with Poynting's theorem? I can tell you how my view is consistent with it in two sentences looking only at Poynting's theorem and without all the red herrings of forces, torques, and pics:

    Per Poynting's theorem, at each location the energy in the EM field decreases (-∂u/∂t) as it does work on matter (E.j) or flows elsewhere in the field (∇.S). Thus, only E does work directly on matter, but B is part of u and S and can do work indirectly through its influence on E and j, just as a tractor may pull a load indirectly through its influence on a rope.
  15. Jun 17, 2014 #14
    Equal to: Esrc = P x t ?
  16. Jun 17, 2014 #15
    If only E does work on matter, show a pic of E spinning the rotor. Oh yes of course, you can't. Maybe E is not doing the work. My pics show perfect compatibility with Poynting, but you just won't see it. If you examine the rotor loop, there are tangential components of both E & B, as well as Fe & Fm. It's all there.

    Fm is q(uXB), and acts in a manner to spin rotor if the rotor is not directly aligned with stator poles. B is due to I/J in the rotor. But I/J in rotor is related to I/J in stator through xfmr-like relation. E acts on primary stator, and Fe = qE, so that Fe accounts for Istator since Fe moves electrons in stator winding. Istator produces Bstator, a mag field.

    Through Faraday induction, stator flux couples rotor, and Fe in the rotor due to Erotor moves electrons in the rotor loop. This Irotor produces Brotor, a mag field surrounding rotor current. So with Bstator & Brotor, we have 2 mag dipoles. Each B is due to I/J & E. E*J is the total work, and the local stator and rotor quantities are subdivisions of said work.

    Fm in the rotor yanks on the moving rotor electrons, put in motion by Fe = qE. The Fm force does not do work on free electrons since direction is normal to electron velocity. But electrons in the rotor material are tethered to the stationary lattice protons via electric force. Fm, the mag force due to B, cannot do work on lattice protons as well because they are stationary. Hence Fm cannot do work on moving electrons, nor stationary protons. Without going into detail, I will state that Fm does no work on the lattice neutrons either, no explanation needed.

    But when the Fm force yanks the electrons in the tangential direction, normal to plane of rotor, the protons get yanked along as well, being tethered to the electrons. Fm could not do work on static protons, but when Fm pulls on the electrons, they yank protons in that direction as well. The protons are being yanked in the same direction as Fm, but not directly acted on by Fm. So is Fm doing the work moving the rotor, or is it the tethering Fe force? As the electrons move, the protons tag along. The energy between the electrons & protons does not change as they move through space. Electric tethering force moves the protons, but for every newton of tethering force from e- to p+, Fm matches it. Fm provides an amount of force equal to the mass*acceleration of both protons & electrons. Thus Fm pulls the rotor tangentially and the rotor turns due to this torque. The Fm force is along the direction of rotor motion, not normal to it.

    Likewise, the neutrons are tethered along with protons due to SNF, strong nuclear force. This force does no work, since nuclear energy is not changed. SNF tethers, but every newton of force expended accelerating neutrons is derived from Fm. Thus the rotor moment of inertia multiplied by its angular acceleration equals the torque on the rotor. This torque is Fm X r, r being radius.

    Imagine a steel sheet with a wood sheet glued underneath, with a plastic sheet held underneath the wood by double sided tape. The sheets are on the floor, an electromagnet is 1 meter above. EM is turned on, the 3 sheets accelerate upward and cling to the EM. Each sheet has a weight of 1 newton. The work done raising this assembly is 3 N-m.

    The EM cannot do work on a lone wood sheet, nor plastic. But the tape and glue provided tethering force so that the EM lifting the steel, which it can do, resulted in wood and plastic sheets rising. The tape and glue do provide force, but it is matched by the EM. EM provided 3 newtons of force to lift the assembly. EM did all the work, even though it could not do so w/o the help of tethering forces.

    Likewise Fm cannot do work on electrons alone, protons alone, nor neutrons alone. With the help of electrical and strong nuclear forces tethering, the Fm force does all the work. Strange for sure. Fm cannot do work on any of the particles in the rotor separately, not even the moving electrons. But with help from tethering forces, it does work in spinning the rotor.

    E forces, Fe, are not acting along the rotor motion. Only Fm is doing that, per my pic.

    Edit: Those who insist that electric forces are doing all the work are also at a loss to explain the motion of the rotor neutrons! Approx. half the rotor mass is neutrons. It is well known that E fields cannot do work on neutrons. So what moves the neutrons? It has to be SNF, no other explanation is even remotely true.

    Clear now?

    Last edited: Jun 17, 2014
  17. Jun 17, 2014 #16
    How can poynting's theorem relate to the Lorentz force?
    Dissipated electric power can be calculated? Why not use P = I^2R?
  18. Jun 17, 2014 #17

    Jano L.

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    Gold Member

    Cabraham, you need to calm down and think a bit more about what DaleSpam has written. As far as I can tell, he is quite right in insisting that magnetic force does no work.

    Magnetic field does work in the older theory of magnetism, where each magnet is made of two poles.

    In standard electromagnetic theory as we use it today, the magentised matter does not contain magnetic poles, only electric currents. Magnetic field does act with force on these currents, but always perpendicularly to them so no work can be done. All work has to be done by electric force. Energy interpretation of the Poynting theorem is based on this.

    Even when two magnets or current loops gain kinetic energy when they act with force on each other, it is the work of electric force that acts on charged particles in them, while changing magnetic field energy in the space around them to kinetic energy of motion and heat.

    Sometimes the presence of electric field may be hard to see, but if work is done, it has to be there.
  19. Jun 17, 2014 #18


    Staff: Mentor

    I cannot, but my graphical and analytical failings are not at issue here. The whole point of doing general derivations from first principles is so that you can reach general conclusions regardless of the details. Frankly, the details are completely irrelevant.

    Poynting's theorem is derived from Maxwell's equations and the Lorentz force law, i.e. the laws of classical EM. So as long as we are dealing with classical EM then Poynting's theorem holds and the work is E.j. My inability to correctly draw or analyze a motor notwithstanding.

    I looked at your pics again to refresh my memory, but it was as I remembered: without any demonstration of compatibility with Poynting's theorem.

    It takes more than simply drawing an E-field to demonstrate compatibility with Poynting's theorem. You have to show that at each point your fields and currents have the precise relationship demanded by Poynting. If you were to actually analyze it that far, i.e. using equations, then you would necessarily see that the work is E.j. Either that or your fields and currents would violate the laws of classical EM.

    That level of analysis is beyond me. Which is precisely why I rely on general derivations like Poynting's. If it is within your capacity then post it. Otherwise I think that my objections to your analogy are reasonable. It appears to conflict with Poynting's theorem, and you have yet to justify it.

    Precisely. There is no work left over for B to do directly. E.j already directly accounts for all of it. If B is to provide energy for doing work, it must do it indirectly through E.j because there is no "missing work" for B to do directly.

    Again, I have no problem saying that B does work (it has energy and that energy can be transferred to matter), as long as you recognize that it does it indirectly through E.j.
    Last edited: Jun 17, 2014
  20. Jun 17, 2014 #19


    Staff: Mentor

    Poynting's theorem is derived from the Lorentz force equation (and Maxwell's equations).

    P=I^2 R is only valid for purely resistive loads and only when circuit theory is valid. Poynting's theorem is more general and applies for any classical EM scenario.
  21. Jun 18, 2014 #20
    He is quite right, but you cannot prove why. Nobody can draw a pic showing E doing work, but they know that it does w/o any proof. Does the word "dogma" come to mind. You claim that E field is hard to see, but if work is done it has to be there. You cannot draw it, you cannot establish the direction, but you assume the very thing you wish to prove then assert said assumption.

    Yes the Fm Lorentz mag force acts normal to currents, but the rotor spins in that direction. Fm is not normal to rotor direction, they align. That is my point. If you look at Fm's direction, it is normal to the moving electrons in the rotor loop, and to the rotor loop current. But it exerts torque on the rotor spinning it. This is work by any definition old or new.

    There is no E force, Fe, spinning the rotor, my pics show both components of E, and they do not act in the rotor spin direction. You seem to be suggesting that E must be spinning the rotor because it is known that B cannot. You're asserting an assumption as proof to your foregone conclusion. Not very scientific. Best regards.

  22. Jun 18, 2014 #21


    Staff: Mentor

    There is nothing dogmatic about it, there is clear proof in the form of the derivation of Poyntings theorem from first principles. The proof is open for anyone to read and understand, with no need to take anything on faith. And it applies to all classical EM regardless of the details of any specific scenario, including motors.

    With that, this thread is closed.
    Last edited: Jun 18, 2014
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