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Electromagnetism and relativity

  1. Apr 9, 2014 #1
    In a video on the youtube channel "Veritasium", it is explained that an electric field and a magnetic field is basically the same thing, it all just depends on which reference frame you are observing it from.

    The video demonstrates that if a positive particle is traveling along side of a wire with the same speed of the electrons running trough the wire, the particle would experience a magnetic force viewed from the wires reference frame. But from the particles reference frame, it would be an electric force.

    In the particles frame of reference, the protons are moving and because of length contraction, the wire would be positively charged. This i can understand/accept.

    But what i can't understand is why there is no force on the particle even though its not moving:
    When the particle is stationary relative to the wire, the electrons are moving relative to the particle. And therefore - with the same logic - the electrons would be contracted, and thus the wire would be negatively charged. (See 1:20 in the movie posted below)

    Why is there a force on the particle when its moving, but not when its stationary to the wire? Why are not the electrons contracted when the particle is stationary to the wire?

    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. Apr 9, 2014 #2

    Simon Bridge

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    I suspect:
    The way the demo is set up, the moving electrons have equal and opposite charge density as the stationary protons when viewed from the frame where the wire is stationary.

    Also see:
  4. Apr 9, 2014 #3
    So that if the current is off, there would be an electric/magnetic force on the particle no matter how fast the particle is moving along the wire?
  5. Apr 9, 2014 #4

    Simon Bridge

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    If you switch the current off, you have electrostatics ... the wire is a conductor so the test charge attracts negative charge to itself.

    The idea is that the classically ideal positive test charge is moving at the same velocity relative to the wire as the classically ideal negative charge distribution in the wire. There is also an equal (but opposite) classically ideal positive charge distribution that remains stationary, relative to the wire, in the wire.

    Still in the Frame of the wire, there is an electric current so there is a magnetic field about the wire and the test charge is moving perpendicular to that field so it experiences a force by the usual rule which pushes the test charge away from the wire.

    In the frame of the charge, there is no current - but the charge measures a net positive charge which has an electric field which pushes the test charge away from the wire.

    Relativity is what happens when different observers meet up to compare notes:
    Observers stationary wrt the wire and those stationary wrt the test-charge agree about the effect, but disagree about the cause.

    You don't have to set things up this way - you could set it up so there is an electric field in both situations if you wanted, it's your imagination but why work that hard? - the point of doing it this way is to highlight how electrical fields become magnetic fields.

    Please see the link.
  6. Apr 9, 2014 #5
    Thank you!
  7. Apr 9, 2014 #6


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    This isn't true by the way, and I don't think the video meant to imply that (of course I absolutely love Veritasium so I may be a little biased here). The magnetic and electric fields are fundamentally different-they are not "basically the same thing" by any means. What relativity shows is: only the electromagnetic field is Lorentz covariant and how the electromagnetic field "decomposes" into electric and magnetic field components depends on the reference frame.
  8. Apr 9, 2014 #7
    So when he says "A magnetic field is just an electric field viewed from a different frame of reference" he is mistaken?
  9. Apr 9, 2014 #8
    Distance between electrons is not contracted.

    Here's a little question:

    Code (Text):
    Cannon1 -->              Cannon2 -->
    Two cannons above are fired simultaneously. What is the distance of the cannonballs when the cannonballs are at the ends of the barrells? Distance of cannons is L. (measured from right end of a barrell to right end of other barrell)

    (If you need the velocity of the cannonballs, it's v)
    Last edited: Apr 9, 2014
  10. Apr 9, 2014 #9


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    If interpreted literally, yes. Unfortunately the standard non-covariant 3-vector treatment through the Lorentz transformations of the electric and magnetic fields that you find in certain EM and SR texts tends to promulgate such thinking. It is not that "A magnetic field is just an electric field viewed from a different frame of reference" but rather that the electromagnetic field decomposes into electric and magnetic field components in different ways relative to different reference frames.
  11. Apr 9, 2014 #10
    Same difference as L?

    So even though the cannonballs are contracted, the distance between them is still L? If this is the case, why isn't this the case with the protons?
  12. Apr 9, 2014 #11


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    This would be like saying that space is basically the same thing as time. Or that energy is basically the same thing as momentum!
  13. Apr 9, 2014 #12
    Can i say that an electric- and magnetic field are manifestations of the electromagnetic field?

    Just as i can say that time is a manifestation of space-time?
  14. Apr 9, 2014 #13
    Because that case is different. Here's one difference:
    A wire or a cannonball can be under stress. A line of cannonballs or a line of electrons can not be under stress. I mean, there isn't any stress if you stretch the distance of two cannonballs or two electrons. What stress means, is that the object under stress wants to become shorter or longer.

    Let's see what is same between cannonballs and wires:
    The protons of a wire form a solid metal object.
    The protons of a cannonball form a solid metal object.
  15. Apr 9, 2014 #14

    Simon Bridge

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    Consider two lines of charges that are moving in opposite directions along the same line in some frame - one is positive and the other negative. Neither forms a solid object.

    In the frame that the positive line is stationary, the negative line spacial separation is such that there is zero net electric field.

    In this frame there is a small positive test charge.

    Now what were you saying?

    @johann1301: you can certainly say that electric and magnetic fields are manifestations of a unified electromagnetic field - yes. The analogy with space-time is apt.
  16. Apr 9, 2014 #15

    Good point.

    Let me elaborate:

    Lorentz contraction in its basic form can be observed or calculated when:

    1: A solid object is gently accelerated
    2: We change to another frame

    Lorentz contraction in its basic form can not be observed or calculated when:

    1: A solid object is accelerated too quickly
    2: A non-solid object is accelerated

    Effects that resemble Lorentz-contraction:

    1: The firing of the two cannons in post #8, but observed from a frame where the cannons are moving, the faster the motion, the more the change of distance of the cannonballs resembles Lorentz-contraction.

    So the case where we first make two lines of charges to move in opposite directions along the same line in some frame, and then we change to the rest frame of the positive charges, can be calculated like this:

    1: The charges are made to move. No contraction.
    2: We change to positive charges' rest frame. Lorentz contraction occurs.
    Last edited: Apr 9, 2014
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