# Inducing Current by Change in Magnetic Flux

Why does a 'change' in magnetic flux induce a current? If we consider a stationary charge placed in a magnetic field, the charge experiences no force (and hence no subsequent motion) due to the magnetic field as it does not have a magnetic field of its own (at least that's what my textbook says). So then, how can the simple change in magnetic field set a charge in motion.

I've seen an answer to the same question I've posed which says that a changing magnetic flux induces an electric field which sets the charges in motion. However, I've looked up another answer which strongly opposes this and talks about Jefimenko's equations (which I haven't understood in the least)

I don't want a mathematical explanation but rather a physical one based on classical mechanics. Something a beginner with basic knowledge of electric and magnetic fields would be able to understand. I know this is a hard ask so I appreciate all attempts made.

... a stationary charge placed in a magnetic field ... experiences no force.

This is correct but draw not the full picture.

The electrons magnetic dipole moment

The electron has a magnetic dipole moment and this moment gets aligned in an external magnetic field.

The electrons intrinsic spin

The electron has a intrinsic spin and due to the Einstein-de Haas-experiment a deflected electron behave like a gyroscope, it changes its direction. For a not moving electron in a stationary magnetic field the alignment of the electrons magnetic dipole moment happens once and no more happens.

The influence of an external magnetic field for a moving electron or a nonstationary external field is more complex. The electron than aligned emit EM radiation and due to the photons impulse the electrons magnetic dipole moment get disaligned again. By this a free in space moving electron slows down and runs in a spirations path until stillstand. Something similar happens in a coil and a nonstarionary magnetic field. It pushes the electrons inside the wire.

Orientation of the electrons magnetic dipole moment and intrinsic spin

All the above said is used in the inductance processes for generators and electric drives. This is possible only because the magnetic dipole moment and the intrinsic spin of the electrons have all the same dependence. (Protons for example are anti-aligned in relation to electrons.)

Consider the following problem: a metal wire is moving through a region with speed $v$ where there is a steady magnetic field $B$ such that it cuts the magnetic lines of force. Because the wire is made up of equal amounts of positive charges (the ionic cores that make up the lattice) and negative charges (the electrons) which are moving in this magnetic field both feel a force, $F = q v B$ where $q = \pm e$. The electrons (being free) move to one end of the wire and the positive charges (being much more massive and being more or less fixed in the solid) are difficult to move. But, there is an accumulation of negative charge one side of the wire and positive on the other, and this looks a little like a battery. With this set up you can arrange to connect (say) a bulb which will light up, showing a current is flowing. Now think about what is happening if you move with the wire. As far as you concerned neither the positive or negative charges are moving so wouldn't expect a current to flow. You explain the current flow by arguing that changes in the magnetic field can cause forces to act on stationary charges. This, more or less, was one of the things that led Einstein to special relativity.

• So basically the answer to my question is slightly more complicated than something that could be fully understood by a high-schooler? Considering the fact that you have to consider special relativity to understand this – LeroyJD Aug 10 '16 at 2:53
• Oh, no. Don't think you have to understand relativity for this. I think it's a case of appreciating that if a charge that moves in a steady magnetic field experiences a force perhaps if you keep the charge steady and "move" the magnetic field something might happen, that is there is some link between electricity and magnetism. – jim Aug 10 '16 at 9:58
• Then the question arises,why does a charge moving in a magnetic field experience a force :p. So basically, it's best to leave the verification of these laws to experimental methods I guess. But one more thing, can a changing magnetic flux PRODUCE an electric field? quora.com/… What does the first answer mean?I can't understand all the math involved. – LeroyJD Aug 10 '16 at 14:57
• I've always been happy to accept the experimental fact that a charge moving in a magnetic field feels a force. As far as the quora.com link, the following may help maxwells-equations.com however the "take home message" is that it isn't quite correct to talk about an electric field and a magnetic field, you should really talk about an electromagnetic field. It's unfortunate, but to really appreciate electric and magnetic fields some maths is needed. – jim Aug 11 '16 at 4:44

I believe you are talking about eddy currents. These can be described using either Faraday's law of inductions or the Lorentz force (this would be more useful in the description of the physical phenomenon).

The Lorentz force is a force caused by a charged particle moving close to the speed of light. Due to the high speed, relativistic effects start to take place and length contraction leads to a higher charge density and a cumulative force called magnetism.

Now that the basic phenomenon has been described it would be useful to get on to why it is the "change" in the magnetic field that causes the currents. If there were no varying field (or a change in magnetic field) then the charges would be at rest relative to the magnetic field resulting in no Lorentz force.

Moreover, you should think about the differences between varying and static magnetic fields. This difference is that changing fields require motion (Motion $\Rightarrow$ Lorentz Force).

I suggest reading a little more about eddy currents and Lorentz force on Wikipedia.

I would also like to add that Faraday's law of induction and Lorentz force law can be unified, but this plays a minor role in the description of the actual physical processes and has more to do with the maths.