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Can magnetic field exist without electric field?

  1. Aug 10, 2014 #1
    Recently I bought - Introducing Relativity A Graphic Guide, in the book, after introducing Maxwell's theory of electromagnetism a line is written, "Simple magnetic fields can occur when there is no electric field (and vice versa)".
    I understand that electric field can exist without any magnetic field, although it is also generated by varying magnetic field, but as much I know, magnetic fields don't exist independently, they are generated by varying electric field or moving charge. Even in any magnetic substance, magnetic field is generated due to electrons orbiting the nucleus, and electrons have their own electric field, so electric field is present their too.
    How is it possible that magnetic field exists without any presence of electric field?
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  3. Aug 10, 2014 #2


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    I couldn't find any direct references to support the idea that a permanent magnet also has an electric field, everything I read said there was only a magnetic field, some one else might.
    I think you will find that any electric field produced by the electrons probably doesn't radiate outside of the permanent magnet. for all purposes a permanent magnet only has a magnetic field

  4. Aug 10, 2014 #3
    Even if electron's electric field is negligible, electric field IS present there, that's what I don't want, I might be misinterpreting the line but I think according to the book, magnetic field can exist even if there is no electric field at all.
  5. Aug 10, 2014 #4
    Neutron has no apparent electric charge and yet it has magnetic moment. But there really shouldn't be any magnetic fields where there are no electric fields, so it is believed neutrons are actually composed of positively and negatively charged particles.
  6. Aug 10, 2014 #5


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    There are two ways of creating an electrical field: Introduce an electrically charged particle, or introduce a time-varying magnetic field.

    However, there are no magnetically charged particles (if they existed they'd be called "magnetic monopoles") so the only way of creating a magnetic field involves some form of electric current or time-varying electric field.

    In that sense, you can't have a magnetic field without an electric field somewhere. However it is possible and indeed fairly common to find a magnetic field at points in space where the electric field is zero, or close enough to zero as not to matter. That's likely what your book meant.
  7. Aug 10, 2014 #6

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    You have to decide if you want to think like a lawyer or like a physicist. A lawyer can complain that there aren't any frictionless surfaces, stretchless ropes, massless pulleys or ideal gasses. And he'd be right. He'd also fail to understand a great deal of physics where these are good approximations.

    You can certainly quibble that nothing is neutral enough for your tastes. All matter is made of atoms and atoms have electrically charged components. But again, you would fail to understand something important.
  8. Aug 10, 2014 #7
    Well I prefer to think like someone curious enough to switch to any point of view necessary because no outlook is useless, I just wanted to know if this was practically possible by some method I was unaware of, but turns out that this too is one of those ideal conditions which are practically probably impossible to achieve, and when I learned that, I accepted that without any question.
  9. Aug 10, 2014 #8


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    Every known charged particle has a magnetic moment, so there are no electric fields without magnetic fields either. There are extremely good approximations to both cases.
  10. Aug 11, 2014 #9
    When we have ideal inductor or ideal capacitor, the current and voltage are out of phase, shifted with +/- 90 degrees.
    So there will be moments in time, when current will be zero at maximum voltage and moments when voltage will be zero at maximum current.
    Without current there is no magnetic field and without voltage - no electric field.


    Last edited: Aug 11, 2014
  11. Aug 11, 2014 #10
    Under static conditions, either can exist w/o the other. A superconducting loop w/ a steady dc current has magnetic field, but no electric field. The counterpart of this setup is a charged capacitor open circuited, as there is an electric field w/o a magnetic field.

    Again these are static conditions, i.e. not changing with respect to time. Under dynamic conditions, i.e. changing wrt time, neither can exist w/o the other. If one field is time-changing, the other must be non-zero.

    Last edited: Aug 11, 2014
  12. Aug 11, 2014 #11
    There is plenty of electric and magnetic fields in wires regardless of voltage. About as much positive as that of negative polarity, so they superimpose and cancel out on average or macroscopically, but microscopically fields are already there.

    I don't think the question is about complex systems, fields cancellation and net result, but really about single elementary particle. I'm not sure whether such particle is necessarily supposed to be a "magnetic monopole" or not.
  13. Aug 11, 2014 #12


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    For any EM field there is a quantity defined at each location: E²-B² which is invariant (a scalar field). If that quantity is negative at some location then there exists a reference frame where the E field is 0 at that location and the B field is non-0.

    I suspect that this is what the book is referring to. I don't think that it is claiming that there is no E field anywhere in the universe, simply that you can have an E field without a B field at a given location, or vice versa.

    Also, in classical EM we typically treat charge distributions as continuous, in which case we certainly can have a neutrally charged wire carrying a current and thereby producing a B field with no E field.
    Last edited: Aug 11, 2014
  14. Aug 11, 2014 #13
    Yes, neutrons have a magnetic field even in absence of electric field.
    Last edited: Aug 11, 2014
  15. Aug 11, 2014 #14
    Yep, you can make magnetic field exist without electric field. Example, any normal bar/horse shoe magnet
  16. Aug 13, 2014 #15


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    FYI, several posts that were better suited to a new thread have been moved.
  17. Aug 13, 2014 #16


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    Hmm... isn't there always a reference frame in which you can find 0 electric field or 0 magnetic field? My special relativity is rusty, but I remember something like that.
  18. Aug 13, 2014 #17


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    Magnetic field can be generated either by a current (moving charge) or by time varying electric field.

    If the magnetic field is generated by a current, it is possible that the electric field is zero or very close to zero. For example the magnetic field from bar magnets is generated by the electrons orbiting the nucleus, while the electric field of those electrons is practically cancelled by the electric field of the protons in the nucleus.

    In the case of a DC current the magnetic field is generated by the free electrons of a conductor which have a net drift velocity, the electric field of the free electrons is again practically cancelled by the electric field of protons of the nucleus of the conductor atoms. What is left is only the electric field of the DC voltage source which also is very small in the region outside the conductor , where in the same region the magnetic field is not zero at all.
  19. Aug 13, 2014 #18


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    Yes. In natural units E²-B² is an invariant. So if it is positive then there exists some reference frame where B=0 and E is minimum, and if it is negative then there exists some reference frame where E=0 and B is minimum.
  20. Aug 13, 2014 #19


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    For a specific point in spacetime, yes - but not for all locations at the same time, at least not in general.
  21. Aug 18, 2014 #20
    The standard answer taught to undergraduates is that yes, you can have a magnetic field without an electric field.

    However, my understanding of the equations and what they really mean is that that's not strictly correct.

    Although you can have a magnetic field without there being any average electric field; you have to consider what a magnetic field really is.

    A magnetic field is not actually a separate field to the electric field; they are one thing, electromagnetism.

    So how does that work?

    Well, when you have (say) electrons moving along a wire, they mostly cancel out the positive charges in the positive wire.

    But, there's a slight wobble in the electric field due to those charges moving; and the more charges that are moving, they on average cancel out over time, but that wobble does NOT cancel out! In fact the more charges there are, the more overall wobble there is. You would think it would be irrelevant, but the electric charge force is so very strong, so even microscopic wobbles in it can have a very big effect when summed up.

    That wobble IS the magnetic field!

    As a pretty good analogy, the equation for angular momentum in gyroscopes has a cross product in it. However, if you look at what that equation is really telling you, you discover that when a gyroscope is turned by a torque there's a slight motion, called a nutation, that invisible wobble is how the gyroscope turns at 90 degrees to the applied force, the wobble moves the gyroscope imperceptibly every cycle; and the result is precession.

    Similarly, that slight wobble in the electric field IS the magnetic field; and that's why there's those funny cross products in the equations relating electric fields and magnetic fields in Maxwell's equations.

    Anyway, that's how I understand it, others will understand it a different way, but to the best of my knowledge, that's what's really going on at bottom, and why it's called electromagnetism, and why Maxwell's equations has all those funky cross products in it.
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