# Induced current in a static magnetic field

I'm a bit confused about magnetism and electromagnetic induction.

On the one hand I understand that to induce a current we need a change in magnetic flux.

On the other... a charge moving relative to an external magnetic field experiences a force. If the field is uniform then we would expect there to be no change in magnetic flux. But will the force on this charge not move the charge and thus produce a current?

Flux is a circuit concept as is EMF. It requires a closed circuit or surface to determine the flux.

Forces on charges are defined by the Lorentz force law and not as a function of flux. They are related to one another through the integral form of Maxwells equations.

The idea of 'induction' comes from experiments involving currents running in wires. The sort of work being done in the 19th Century by Faraday and others.

But when you start to talk about charges moving, you've jumped forward 100 years and some of the old language doesn't quite sit right.

A moving charge isn't the same as current in a wire in the sense that it can move sideways, whereas the current can't - it has to stay in the wire.

So you get the 19th Century idea that 'induction requires a changing B field (or movement of a wire through a B field) Which is true if you're talking about wires and magnets.

And you also get the Lorentz Force F = q(E + vxB) which works for a charge moving freely in space. Both are equally true but the latter is more general.

Thanks Antiphon and AJ Bentley. This has helped me a lot, I'll need to keep thinking on it to process everything you've said.

AJ, I'm thinking that when you say "the latter is more general" I could also assume that the former (induction required a changing B-field) is more useful or has more real applications?

The force on the charge is not a current because it cannot be collected and looped in a wire. The charges on the up side of the loop will experience a force in the opposite direction, so nothing moves therefore no current.

I could also assume that the former...is more useful or has more real applications?
That's a fair statement.
The former is about wires and magnets, industrial stuff.
The latter assumes you have a free charge (electron or whatnot) floating in space in the presence of fields. Outside of the Lab it's not a common situation. On the other hand, it's a compact statement of basic truth.

You get this a lot in electrodynamics - Maxwell's four succinct equations are the formal statement of Physics but for mundane situations one turns to their earthier counterparts - Amperes Law Biot-Savart etc..

Thanks Curl and AJ. I've been doing some reading and I came across some similar information.

A current can be generated in a loop that is in a static magnetic field as long as part of the loop is outside of the field. (If all of the loop is in the field then the movement of charges on one side of the loop is opposed by the movement of charges on the other side.)

Elsewhere I've read that "a current can be induced in a conductor by either the motion of a conductor through a magnetic field or a change in the magnetic field around the conductor." So this seems to say that both of the conditions I initially asked about can produce a current, but we have to keep in mind the point made by Curl.

I'm now wondering why a change in flux can produce a current in the loop when a static field cannot. I'm thinking that this is because there is a difference in the field on either side of the loop so the forces do not cancel... this is probably a big over-simplification, but it's something I can work on.

Thanks again for the help.

I'm going to hit you with a big one.

You are probably thinking of the Electric and Magnetic fields as two distinctly separate things?

They are not - there is only one field and it's called the ElectroMagnetic field.
The apparent difference that we perceive is down to Einstein's relativity. A magnetic field is the aspect of the EM field that you experience when movement is involved. The effects of relativity are so strong in the case of EM that we can observe them even at our normally low speeds (unlike say the change in mass of high-speed objects).

You see magnetic effects when charges move ( a current) or when you change the intensity of an electric field. Anything involving movement or change of electric field.
Conversely, when you have a moving magnetic field, you get electric fields being created - The whole thing is beautifully symmetric.

The equations which describe this situation are known as Maxwell's equations and are amongst the most elegant and fascinating parts of this subject.
Unfortunately it requires a hard slog through the Swamp of Dire Mathematics to get to them. It's worth it in the end but boy! is it hard going.