# How does magnetism induce current

1. Aug 9, 2009

### Red_CCF

Hi, I have a couple of questions here:

1st, I never really understood how magnetism induces current, like how does magnetic fields just suddenly cause electrons to flow.

Another question I have is on how transformers work (the electric device, not the robots). I looked at some explanations and images of transformers and I don't understand how magnetism induces a current of lesser voltage in a transformer as it's circular and has no defined poles?

2. Aug 10, 2009

### diazona

Well, you'll first need to understand how magnetism induces a current before you can understand transformers. Not why, necessarily, but how.

In order for a magnetic field to induce a current, the magnetic field has to be changing, relative to the wire. So the field could be getting stronger, or weaker, or the wire could be moving relative to the field, etc. The point is, it's that change that induces the current. One common way to remember this is Lenz's law, which says that the new magnetic field produced by the induced current "tries to" cancel out the change in the original magnetic field.

If the above seems a little hand-wavy to you, that's probably fair. In a sense, it all comes from the Lorentz force law, which describes the force on a particle in a magnetic field:
$$\vec{F} = q \vec{v}\times\vec{B}$$
or, roughly, force is charge times velocity times magnetic field. But to get from that to what I said in the previous paragraph in a really believable way takes a fair amount of dense math.

As for transformers, here's a very rough description: the current that flows through the end of the transformer that's hooked up to the power station is always changing. (Since it's AC, not DC, the current switches direction 60 times a second) That means the magnetic field produced by that current is also always changing, and in turn that constantly changing magnetic field produces a current in the wire at the other end of the transformer.

3. Aug 10, 2009

### bm0p700f

I think Red want to know why magentism induces current on a more fundamental level. Your post covers Lorentz law and is presented in the way you find in every physics text book. This Law allows you to make useful prediction about how a charge behaves inside a magnetic field. But this does not address what is the fundamental mechanism for inducing current. Its a bit like asking what produces a magnetic field. In most text books they will describe how a current generates a field and talk about Biot-Sieverts Law. This does not address fundamentally what magnetism is. For that you have to look a special relativity.

4. Aug 10, 2009

### Staff: Mentor

A changing magnetic field produces an electric field, according to one of Maxwell's fundamental equations for electromagnetism:

$$\vec \nabla \times \vec E = - \frac {\partial \vec B} {\partial t}$$

The induced electric field exerts a force on the charges in the wire, which makes them move and produces a current.

5. Aug 10, 2009

### I_am_learning

Yeah, As jtbell has indicated, the changing magnetic Field (that induces current) is nothing but an electric field. If you go on to relativity you will learn that magnetic field and electric field are inter-related. What appears to be a magnetic Field may appear as electric Field to some other frames of reference and may appear as mixture of both to some others..

I Guess, that every electromagnetic phenomenon can be totally described either by electric fields and electric charges OR totally described by magnetic field and magnetic poles. Am I right at this? please let me know.

6. Aug 10, 2009

### Bob S

I have never really understood how a transformer worked in terms of the Lorentz force for a couple of reasons. 1) Ideally in transformers, the magnetic field is entirely inside the iron laminations. You imply that the transformer coils are also in the magnetic field. Is there a leakage magnetic field in the coils which leads to the use of the Lorentz force? 2) Since the Lorentz force is a dc force, does this mean I can transform 12 volts dc to 6 volts dc in a transformer? How?
Thanks.

7. Aug 10, 2009

### Red_CCF

Thanks for the replies

Yeah that was what I was getting at. I don't really understand how a changing magnetic field cause electrons to move within a wire and why the magnetic field must be changing to produce a current. But if the explanation involves relativity and quantum mechanics I'll probably leave it alone for now because it'll be too advanced for me.

Thanks for the help

8. Aug 10, 2009

### Naty1

Neither does anyone else!!! If you want to go beneath the level of all the formulas for electromagnetic induction and those of frames of reference in relativity was well, it's likely nobody really understands it at a truly fundamental level. Maxwell's equations relate the electric and magnetic fields to the motions of electric charges.

We don't even know what an electron is, nor why there are not magnetic monopoles all over the place. A 1931 paper by Paul Dirac showed theoretically that IF magnetic monopoles exist, which have not yet been experimentally confirmed, then that would explain the quantization of electric charge in the universe...so we don't even understand why electric charge is quantized. (Maybe QM has a better understnading now??) Polchinski says the existence of monopoles is "one of the safest bets that one can make about physics not yet seen".

Its sort of akin to asking why space and time vary but speed of light is constant....nobody really knows but we have a lot of slick math to describe and predict interactions....if space and time did not vary, electromegnatism would not "work". Hence we would not be here. So it seems a requirement for this universe. We don't really know why an electric field "transforms" to a magnetic one from a different frame of reference; does anybody even know why the two fields are orthogonal??....besides experimental results?? I don't know if there is any fundamental explanation for that either.

Wikipedia has a decent description of transformers and diagram with basics at
http://en.wikipedia.org/wiki/Transformer#Detailed_operation

9. Aug 14, 2009

### bjacoby

The above explanation while commonplace is not correct. The truth is that a changing magnetic field does not produce an electric field! Oleg Jefimenko in his book (see Amazon) "Causality electromagnetic induction and gravitation" has shown that while the above equation is a correct relationship between a magnetic field and an electric field, it is NOT a causal relationship as is widely assumed. Nor does the Lorentz relationship provide an "explanation" for magnetic induction. Proof of this is that induction occurs in regions where there is no magnetic field! These include outside a toroid or down the length of a straight wire. Clearly straight wires do have self-inductance.

The correct relationship is along the lines of the Neumann formula. In other words an element of current that is changing in time creates about itself an electric field that is either in the same direction as the current element or in the opposite direction. The distribution of the electric field is spherical and falls off as 1/R. The relationship is simplified by use of the magnetic vector potential as an intermediate stage.

The key point here is that a changing magnetic field DOES NOT "create" an electric field per the Maxwellian relationship. What happens is that a changing current creates BOTH the induced electric potential in space about itself (traveling outward at the speed of light) as well as a magnetic field which is created at the same time (also traveling outward at the speed of light). The two are related but do not "cause each other".

I have attempted to correct the errors in Wikipedia in this regard but the editors appear unwilling to examine the mathematics establishing the truth of Jefimenko's (and Panofsky's) assertions. The primary argument seems to be that "everybody knows" that electric and magnetic fields create each other.

10. Aug 14, 2009

### Bob S

Jbell's explanation, describing Faraday induction, correctly describes how a particle accelerator called a betatron works. The beam is confined to a small beam tube surrounding a large area through which a large dB/dt is created. This area is like one square meter of dB/dt at 60 Hz. This induction produces a continuous azimuthal accelerating electric field inside the beam tube that accelerates the electrons to 100's of millions of volts (100's of MeV). See
http://teachers.web.cern.ch/teachers/archiv/HST2001/accelerators/teachers notes/betatron.htm

11. Aug 15, 2009

### bjacoby

I have quoted your post because your statement that Jbell's equation correctly describes how a betatron "works" is not incorrect. The equation does indeed describe relationships to some degree between the magnetic field and the induced electric field in the acceleration doughnut.

A betatron is a bit of a bad example because they usually have an iron core to increase efficiency which complicates discussions. But lets assume for the sake of argument there is no iron core. We have a large coil of wire and an acceleration doughnut. Hence the coil is in essence a primary winding and the electron beam the secondary winding of typical air-core transformer.

There is no doubt that the change in the magnetic field through the hole in the doughnut is mathematically related to the E field inside the doughnut that accelerates the electrons. But a relationship is not causality. Indeed consider what is called "retardation". What is the delay (at the speed of light) from the current at a given spot in the wire of the primary coil, and the E field inside the doughnut? The current element creates a magnetic field that travels away from the current element at the speed of light. Does that magnetic field then create an E field that travels to the doughnut at the speed of light by some path? No it doesn't. The E field doesn't travel along magnetic lines of force or any such thing. The E field is created by a retardation on a straight line between the source current and the place where E is measured. And does so at the speed of light. The magnetic field at that point also does the same thing. Hence both are simultaneously occurring.

If one accepts causality as a rule in physics one must accept that things which occur at the same time cannot be the cause of each other! Causality demands that action is preceded by the cause. If you look at Jbell's equation you see that both E and B are simultaneous. They may be related, hence they form a useful relationship that can measure how something "works" but the equation does NOT imply that either field is the CAUSE of the other. This can only mean, per the original question in this thread that magnetism does not create an E field so that it cannot induce a current to flow. The current is induced directly (in retarded fashion) by a source current which also creates a magnetic field (likewise retarded) at the same time.

However, note that our discussion here is limited to transformer actions such as a betatron where there is no relative motion involved as there is in the case of generator actions.

12. Aug 15, 2009

### Bob S

Hi bjacoby-

You have brought up some interesting points in your post. The betatron is actually a very good example of magnetic induction, because in this case the electric field is in vacuum (free space), and not constrained to a wire, like in a transformer.

First, I would like to discuss retardation and signal propagation in magnetic materials. As you probably know, signals in vacuum travel at the speed of light; c = 1/sqrt(ε0μ0), where ε0 and μ0 are the permittivity and permeability of free space. In glass, the apparent speed of light is 1/sqrt(ε ε0μ0) = c/√ε = c/n, where ε is the relative permittivity of glass, and n its index of refraction. The same thing happens in magnetic materials. The speed of signal propagation in a ferromagnetic material is v = c/√μ, where μ is the relative permeability. For soft iron and transformer iron, μ ≈5000, so v ≈ c/70 (neglecting other factors). So the signals travel through iron √5000 = 70 times (or more) slower than the speed of light. So any signal traveling from the primary coil to the secondary at the speed of light must be traveling independent of the presence of the iron. But would there be a signal without the iron?

This delay can be demonstrated in a torus. Consider a flexible ferrite torus of major radius 5 cm, minor radius 3 mm, and μ =5000. Put several turns of wire on the right hand side, and several turns on the left. A fast pulse of the left hand side will take about 36 nsec to reach the right side via the ferrite, vs. less than 1 nsec by direct speed of light propagation. Now visualize the following: Pick up the torus with each coil between your forefingers and thumbs. Now twist the coil in your right hand 90 degrees so that the planes of the two coils are orthogonal. Will there still be a pulse traveling from the left coil to the right coil, and if so how did it get there, and how fast? If the ferrite torus were removed, there is no coupling from one coil to the other because of orthogonality. So the signal either travels inside the ferrite, or on its surface, but is not line of sight. It has to be causal, because with no ferrite, there would be no signal.

In jbell’s equation, the ∂B/∂t in the iron at the beam torus in the betatron creates the longitudinal (accelerating) E field in the beam tube torus. This is a causal relation (see above). Furthermore, a DC (fixed) E field outside the iron cannot create a ∂B/∂t inside the iron (∂B/∂t = -curl E). The ∂B/∂t at the beam torus is retarded from the ∂B/∂t created in the iron at the primary coil, and travels to the beam torus at the velocity c/√μ. So the E field in the beam torus must be caused by the ∂B/∂t field in the iron, and not by direct coupling to the primary coil.

Bob S

13. Aug 16, 2009

### bjacoby

Bob S is determined to bring magnetic materials into this discussion and make it more complicated even though I've been trying not to discuss that.

I'll say this much: A current element creates a magnetic field that travels outward at the speed of light. Such a field in a magnetic material induces magnetization per unit volume in that material according to what it is. This induced magnetization takes some time to be produced and hence means that the action is slower (as Bob S calculates) could be 70 times slower than the speed of light. This magnetization creates a secondary field which adds (or cancels) the original field. People say that the magnetic field is concentrated in the Iron and zero (or low) outside the iron, but that may not strictly be true. It's only true if you accept that magnetic fields actually truly cancel each other. (but that is another story). The point is that you have two fields which cancel in some regions and add in others. One field is due to the original current and the second field is due to the induced magnetization. To the outside observer it appears as if the magnetic field is concentrated in the iron and does not exist outside the iron. It certainly measures zero out there, but that does not mean there may not be experiments other than a gaussmeter that might show both fields uncancelled.

Some points to consider here are that basically ALL magnetic fields are caused by currents. The magnetic fields of the iron are caused (supposedly) by circulating currents in the atoms. Note that while there is a delay in the magnetization taking place, once it is established, the secondary magnetic field proceeds away from it's source ALSO at the speed of light! Thus the effect of the iron in slowing transmission of magnetic effects does not actually slow the magnetic field propagation. There is just a slow intermediate step in the middle.

So in your toroid example we find that the driving coil does indeed produce a magnetic field at the secondary coil which may or may not be sensed according to it's orientation (the induced E field must be parallel to the wire to produce a voltage or current). But that field also produces (at a later time) magnetization in the toroidal core. Then that magnetization due to the circulating currents in atoms in turn produces a secondary field which travels outwardly. That field can be measured with a gaussmeter. However if you are using a coil to pickup up the secondary field one must assume that it is NOT the dB/dt of the secondary field that is causing the induction. For one has exactly the same situation now as one had without the magnetic materials. It is the change in the circulating currents in the material that is creating the induction NOT the "magnetic field".

The reasoning is that while there is a delay between the circulating currents and the inducting field, the transmission of action between the circulating currents and the secondary coil are transmitted at the speed of light. Hence the B field and the E field still arrive together (which is what Maxwell's relation shows) and hence cannot be "causing" each other.