# Moving magnetic fields?

I was reading through Feynman Lectures on physics vol II when I came across this paragraph which I don't quite seem to understand:

Since electric and magnetic fields appear in different mixtures if we change our frame of reference, we must be careful about how we look at the fields E and B. For instance, if we think of “lines” of E or B, we must not attach too much reality to them. The lines may disappear if we try to observe them from a different coordinate system. For example, in system S′ there are electric field lines, which we do not find “moving past us with velocity v in system S.” In system S there are no electric field lines at all! Therefore it makes no sense to say something like: When I move a magnet, it takes its field with it, so the lines of B are also moved. There is no way to make sense, in general, out of the idea of “the speed of a moving field line.” The fields are our way of describing what goes on at a point in space. In particular, E and B tell us about the forces that will act on a moving particle. The question “What is the force on a charge from a moving magnetic field?” doesn’t mean anything precise.

But later in another chapter on induced currents he talks about how moving a wire perpendicular to a magnetic field produces a force on the electrons which cause them to move along the wire, generating a current. But he also mentions that moving the magnet itself(and hence it's magnetic field) in the direction opposite to the direction the wire was previously moved produces the same force on the electrons.

• Are the words "and hence the magnetic field" yours, or Feynman's? If they are Feynman's, please provide the entire quote and context. Nov 8, 2015 at 13:47
• They are mine. If a magnet moves, won't the magnetic field move too? Nov 8, 2015 at 13:59

You say "and hence the magnetic field" moves. No it doesn't, and that's exactly the point Feynman is trying to make.

Read it carefully. He considers the magnetic field to be a property of space, so to speak. At each point in space there is a magnetic field. It's magnitude and direction can change, but the field at that point is fixed to live at that point. The field at a point can change, and the field at the point's neighbors can change in such a way that the pattern of the field moves (a wave). But the field itself does not move.

I am a novice, but I thought with that tokamak the scientists are making, that they devise some magnetic field in addition to what they have to sort of pull the plasma along on the outside where the (ELM) edge localized modes are occurring. Maybe spin a permanant magnet nearby so the eddies don't form. They could try spining a magnet backwards to comb the eddie current back in.

Consider a horseshoe magnet with opposing poles (faces) and a magnetic field in the region between the poles. A loop of wire is moved through the field from one side to the other, its area broadside to the field. Now instead, let the loop be still and the magnet moved the opposite way. Magnetic flux enters one side of the loop, travels across, and exits the other side. What is true of flux here is true of flux density, which is B. \$10 to the first person who can convincingly argue that the field did not move. By the way, Feynman was not God.

I see two negative votes to my comment but no actual arguments. To say that the field doesn't move but only the pattern does is just a tortured distinction without a difference. We see this also in Feynman when he refers to a "traveling" (electromagnetic) field but still tries to distinguish it from a moving one. He goes on to an analogy with a wave on a string in which the displacement of the string appears here now and there later, but the string itself doesn't move. It's a poor analogy because nothing in electromagnetism corresponds to the string itself, but even setting that aside, if the transverse displacement of the string corresponds to the field, well, that displacement clearly does move from place to place, just like the field does.

"Field lines" are a convenient way of representing field and flux. The force exerted on a stationary charged particle by a moving magnetic field has every bit as much meaning as the ("Lorentz") force on a moving particle in a stationary magnetic field. To the best of my knowledge, all examples of induced emf are explainable by motion relative to a magnetic field.

To be a bit more technical: What is conventionally regarded as an electric field can arise from a combination of two things: the gradient of the scalar potential, and the partial time derivative of the vector potential. The former is sourced by charge distributions and can cause no emf around a closed loop. The latter is sourced by currents and is easily shown to be due (in a given frame of reference) to a moving magnetic field. In combination with the conventional Lorentz force law on a moving charge, this demonstrates that induced emf can be viewed 100% as a magnetic effect. It does not have to be seen mysteriously as a magnetic effect in one frame and an electric effect in another frame.

Nothing said here is intended suggest that there is something wrong with explanations and problem solutions involving Lorentz transformations of the electromagnetic field tensor (although this is not something I would have inflicted on my intro physics students). There are multiple perfectly valid ways of modeling electromagnetic and other phenomena. They should not be dogmatically dismissed.