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Why do Parallel Currents Attract?

  1. Aug 15, 2004 #1
    I've read that when currents in two parallel wires are going in the same direction, they attract each other. The same text said that when the currents are going in opposite directions, the two wires repel each other.
    Why does this happen? Is there a different behavior for AC and DC currents?
  2. jcsd
  3. Aug 15, 2004 #2
    its because of the right hand rule, which describes how magnetic fields/the magnetic force work
  4. Aug 15, 2004 #3
    Please explain with a bit more detail. Thanks!
  5. Aug 16, 2004 #4
    let's say that there are two wires, with their current mving towards us from a far place. The wire on the left generates an upward magnetic field at where the wire on the right is. Using Fleming's left hand rule, we find that the electromagnetic force acting on the wire on the right is directed towards left. Vice versa applies, and the wire on the left is pushed towards the right by another electromagnetic force. This makes it look like an attraction.
    When the currents move in opposite directions, the eletromagnetic force causes them to repel each other in a similar way. You can work it out yourself :)
  6. Aug 16, 2004 #5
    If the two wires are side-by-side wouldn't the magnetic force of both wires point upward toward the ceiling?
  7. Aug 16, 2004 #6


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    No, the magnetic field of a wire 'curls around' the wire with the direction given by the righthand rule:
    Curl your fingers slightly. If your thumb points in the direction of the current,
    your fingers point in the direction of the magnetic field.

    The direction of the magnetic force on a charged particle or current is also indicated by
    a right-hand rule. If your fingers curl from the direction of the current to the
    direction of the magnetic field over the smallest angle, your thumb will point
    in the direction of the magnetic force.

    So imagine 2 wires drawn vertically on the board with current flowing upwards.
    The magnetic field of the right wire points out of the board at the position
    of the left wire. Then the magnetic force on the left wire points to the right.
    Same kind of argument shows the that force on the right wire points to the left.

    In AC currents, the direction of the current changes all the time, but it
    still flows in the same direction in both wires at any given time.

    This has to do with perspective. Parallel lines seem to merge in the distance, but the distance will remain the same. It has nothing to do with physics.
  8. Aug 17, 2004 #7
    If the magnetic field is the cause for the attraction, then what property of the magnetic fields actually produces the attraction?
  9. Aug 18, 2004 #8


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    A magnetic field exerts a force on a moving charge:
    [tex]F_{mag}=q(\vec v \times \vec B})[/tex]
    This is the Lorentz Force Law.
  10. Aug 18, 2004 #9
    If you have two vertical wires with current moving up them, then the left side of the wire is the north pole and the right side of the wire is the south pole (N / S N / S). Opposite poles attract, right?

    Now, let's run the current down the right wire instead of up. The poles on the left wire remain the same while the poles on the right wire have reversed (N / S S / N). Like poles repel.

    If you use AC fed into the same end of the wire, they will attract. If you feed AC into opposite ends of the wire, they will repel.

    Same End /\/\/\/\ Opposite Ends /\/\/\/\

    (Note: Of course, you need a complete circuit for current to flow)

    Try to keep it simple, guys.
    Last edited: Aug 18, 2004
  11. Aug 18, 2004 #10


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    Another way to look at it is that currents obey an inverse square law, just like masses and charges.

    It's just, because currents are vectors instead of scalars, you have to use the dot product instead of ordinary multiplication.

    \vec{F} = C \frac{\vec{I}_1 \cdot \vec{I}_2}{|\vec{r}|^2} \hat{r}

    I forget what the constant C should be, but it's negative.

    Of course, this is only exact in the static case, or when you can otherwise ignore the propagation delay of the magnetic field.
  12. Aug 18, 2004 #11
    I think what_are_electrons is wanting to know what distinctive characteristics of magnetic fields gives rise to attraction. What make two fields attract or repel? He is not wanting equations (I'm assuming...), but he is wanting an explanation of how forces are able to attract or repel. The equation just tells whether or not there will be attraction or repelling. If he doesn't want a more descriptive answer, I sure would like to know. So, can anyone answer me this?
  13. Aug 18, 2004 #12


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    There are some interesting remarks one could make about the magnetic field being a sort of relativistic correction to the columb field, but it would be hard to express these comments in very elementary & simple terms that are being asked for.

    So the best that can be said in simple terms is that magnetic fields exert a force on moving charges according to Lorent'z force law. I could provide a link to the details of this law, but it seems that that's not really the question being asked - if anyone is interested, I can say more about this law. One also has to realize that a current consists ultimately of moving charges to appreciate this explanation in terms of the Lorentz force law. A current in a wire actually consits of some charges that are moving, and some charges that are not. Fortunately, the non-moving charges don't generate any force by the Lorentz force law.

    Perhaps "what_are_electrons" is attempting to ask a philosophical or metaphysical question. In this case, the philosphy forum would be more appropriate. From a scientific point of view, we can explain what things do. One can talk a bit about the history of how things were discovered, i.e. how the magnetic field of a current was discovered when someone noticed a compass needle moving near a wire carrying a current. We can even offer differing models, some of the more elegant models require a bit of sophistication and learning of the simpler models to appreciate. But science can't answer the philosophical questions, which generally have the tendency to go on and on and on, because they basically don't make any difference to results that can be measured.
  14. Aug 18, 2004 #13
    I kind of remember reading somewhere that a magnetic field occurs due to synchronized electron spin throughout a conductive material. From the spin there are virtual photons emitted and these become force carriers.

    Any material with enough electrons with the same spin (or could be made to have the same spin [permeable]) would be attracted. Any material with enough electrons with an opposing spin would be repelled.

    I don't know if this is true, but it sure sounds good.
  15. Aug 18, 2004 #14
    The North-South pole attraction for parallel current flow explanation is exactly what I think is true.

    The question that follows is:
    If a current flow produces a magnetic field (actually an EM field), then does that mean that a solid magnet (natural lodestone mineral or an electomagnetized magnet) has some sort of electric current? Is there a current flow within the static magnet? Is that current due to synchronized electron spins?
    Last edited by a moderator: Aug 18, 2004
  16. Aug 18, 2004 #15
    Metallicbeing, when you are referring to the spinning of electrons, are you referring to their spin in the orbitals? Could you provide me a link stating this also? It sounds interesting.
  17. Aug 18, 2004 #16


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    This explanation would not properly explain the observed deflection of an electron beam in a cathode ray tube. The Lorentz force law correctly predicts that the force on a moving electron inside a CRT increases with the velocity of the electron ( F=q(v x B) ). An attempt to explain deflection of an electron beam based on its magnetic moment will fail because

    1) it wouldn't give a large enough force to match observed results
    2) it wouldn't give a force proportional to velocity
    3) it would predict that an electron beam would have to generate two spots on the screen, one spot for each orientation of the magnetic moment, like the stern gerlach experiment does with silver ions.

    In actuality, we observe the forces due to the magnetic moment of the electron are so small that they do not resolve the spin of the electron, the Lorentz force by far dominates any force due to the magnetic moment.
  18. Aug 18, 2004 #17
    In everyday materials, electron spins are randomly orientated, leaving no organized field. Permanent magnets were created in the presence of a magnetic field while they were in viscous form then allowed to solidify. It would seem that only ferrous type materials are capable of keeping a synchronized spin with no electron current flow present. If there is any current flow at all, then it would be in the form of small eddy currents.
  19. Aug 18, 2004 #18
    I'm sorry. I read this some time ago. Maybe you can google it under "What is magnetism". If I recall correctly, that's how I found it.
  20. Aug 19, 2004 #19
    The CRT involves just a single beam of electrons, so I don't quite seen the connection. Am not that familiar with Lorentz law as applied to free electrons in UHV.
    Correct me if I'm wrong, but wouldn't free electrons in a CRT act different from the free charges flowing in two wires that have equal currents? Don't the actual electrons move very slowly in wires (ca. cm/sec) not 10e7 m/s like free electrons in the CRT?

    Since we are talking about charges moving in wires vs electrons moving through space, can we apply the same laws?

    The Stern-Gerlach experiment is an interesting experiment, but it may be that other factors were at work in that experiment. Why is it they used a beam of Ag atoms (not ions as you suggest)? Silver in atomic form has a 4d9, 5s2 electron configuration, only one unpaired electron in a nearly filled shell.

    My 1985 2nd edition of Polarized Electrons by J. Kessler (Springer Verlag) states on p2:
    "Conventional spin filters, the prototype of which is the Stern-Gerlach magnet, do not work with free electrons. This is because a Lorentz force, which does not appear with neutral atoms, arises in the Stern-Gerlach magnet. This, combined with the uncertainty principle, prevents the separation of spin-up and spin-down electrons."

    This book includes discussions on obtaining polarized electrons from unpolarized materials, generating polarized light from polarized electrons etc. Quite fascinating.
    Last edited by a moderator: Aug 19, 2004
  21. Aug 19, 2004 #20


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    I've posted some of the equations relative to dipoles and the forces on and between them in another thread, because I thought they might be interesting and it was something constructive.

    You are absolutely right that a free electron cannot be separated out by a Stern-gerlach type experiment. This is a somewhat obscure point that not many people know about, it originated with (I believe) Bohr. As far as whether or not the experiment used ions, or atoms, I think you're probably right about it using atoms, but I didn't find a definitive reference.

    I missed the most obvious reason that the electron spin explanation won't explain a CRT- a magnetic dipole only expeiences forces from a changing B field, not a static B field. Obviously, static magnetic fields do affect the electron beam in a CRT. If you have one you're not terribly fond of, you can even try putting a magnet near the CRT and watch what it does to the beam. But don't blame me if it messes up the focus and resolution :-).

    A wire contains a lot of slowly moving charge, the electron beam contains fewer but faster moving charges. The wire also contains stationary charge, which eliminates the electric field. However, there is no force on the stationary charges due to a magnetic field, so they can be ignored.

    The Lorentz force gives the force on a single moving charge is F = q(E + v x B).

    If we have a wire with an area A and length L, the current will be n*e*vd*A, where n is the electron density / unit volue, see


    The product of the current and lenght, I*L will be


    So we expect the Lorentz force on a wire of length L carrying a current A to be the force on a single electron with a velocity of vd, multiplied by the number of electrons in the volume A*L, which is n*A*L


    F = (n A L) * e * vd * B

    This can be re-written as

    or F = I * L * B

    This is exactly the result from
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