Induction: How does the electrons in the coil know in which way the magnetic field is moving?

Question

It is well known that a coil will react to a moving external magnetic field in such a way, that the electrons inside it will start moving to produce an internal magnetic field, which counteracts the movement of the external magnetic field.

One question has struck my mind though; in order for the electrons inside the coil to flow in the right direction, they will have to "know"

1. The alignment of the external field.
2. The direction of movement of the external field.

Since the external magnetic field extends into the coil, it is not so hard to imagine the electrons "knowing" the alignment of the external magnetic field. What I don't understand is how the electrons can "know" the direction of movement of the external magnetic field, unless the movement in itself generates a field of some sort?

I have been thinking quite a bit on this, and the only clue that has struck my mind is that as two magnetic fields (aligned in the same way) approach other, the individual field lines slowly rotate versus each other, and goes from being opposite, to being aligned.

I have not studied physics at any higher level, so I would appreciate if you try to keep your answers as non-mathematical as possible.

Answer 1

First, magnetic fields don't move. Every point in space has a (possibly zero) magnetic field vector at that point. And that vector at that point can change in time.

Electrons and other charges react to the electric field vector at the location of the charge and to the magnetic field vector at the location of the charge. They do not react to vectors at other locations.

And the vectors don't move from one location to another. There is a vector at each location at each time. Multiple locations could have vectors of the same size and direction, and a location could even have a zero vector. That's all OK.

Now, about changing magnetic fields (such as those associated with moving magnets, a magnet is a device, a magnetic field is when you have a vector at each location). Time changing magnetic fields are associated with particular arrangements of electric fields.

It's not entirely wrong to think of the arrangement of the electric fields being the cause of the change in the magnetic field. But really the two happen together, so there isn't really any evidence for one causing the other.

On the other hand, unlike an object that can have a position and a velocity and the velocity tells you how it is going and which can be affected by forces which then indirectly change the location by changing the velocity and the velocity changes the location. Unlike that, when you have an arrangement of electric field vectors throughout space and an arrangement of magnetic field vectors and some electric current then the arrangement of electric field vectors forces the magnetic field vectors to change a certain way (so it's like the velocity of the magnetic field isn't free to be adjusted, it is determined by the electric field, but it isn't moving, the vector at each point can change or stay the same), so unless the electric fields are balanced in a perfectly static way, then the magnetic fields have to change in time (though that's different than moving). And the arrangement of magnetic fields, unless it perfectly balances the electric current, it will result in the electric field changing (so it's like the velocity of the electric field isn't free to be adjusted, it is jointly determined by the arrangement of magnetic field vectors and the electric current but the electric field isn't moving, the vector at each point can change or stay the same).

So you can have an electric and magnetic field vector at each point. And unless the arrangement is in perfect static balance, the fields will change. But an imbalanced electric field (one with a net circulation) determines the rate the magnetic field changes. And an imbalanced magnetic field (one with a net circulation different than the electric current) determines the rate the electric field changes.