When a conductor is cut by the lines of flux of a time varying magnetic field, a voltage will be produced in that conductor (assume everything is oriented correctly here). So for example, in a transformer, the primary coil generates a time-varying magnetic field in accordance with the applied AC. This forms a magnetic circuit in the xfrmer core with the flux travelling through the core of the secondary coil. This flux in turn induces a voltage in the secondary coil. Makes sense so far.
…Except, I thought, in the ideal case, there is no leakage flux out of the core. In this case, the flux is contained entirely within the core, and therefore cannot cut the coils that wrap it (since they are external to the core). Put another way, where is the flux cutting the coil coming from if its supposedly contained entirely within the core?
There’s obviously something I’m not understanding here…could any explain?
You’ve just encountered the mystery of “flux linking” versus “flux cutting.”
When a current is induced in a closed circuit, the current isn’t caused by field lines cutting across the wires. Instead, the current is caused by changing value of flux within the circle enclosed by the closed circuit. The flux through the center ofthe circle might be changing because flux lines are cutting across the boundary. But that’s not required.
In other words, you can induce a current by simply changing the strength of flux that’s passing through the “donut hole” of a closed circuit. That flux doesn’t need to be anywhere near the actual wires.
Another way to view this: whenever a magnetic field is changing, the field induces a voltage in the space around itself. Also, this voltage-field doesn’t need to be in the volume of space which contains the magnetic field, instead the voltage field can surround the region of magnetic flux. If you then pass a wire through the voltage field, and bring the two ends of the wire near each other, there will be a voltage difference across the ends. (Well, there’ll be a voltage if your wire encloses some changing magnetic flux.) If you touch the ends together, there will be a current.
So, magnetic fields really don’t induce currents directly. Instead the magnetic field creates a voltage field, and the movable charges inside the wire are then pumped into motion by that voltage field.
One result: an iron core with a vibrating magnetic field inside will have a certain AC voltage in a loop around itself. Pass a wire around the core, and you see that value of AC voltage. But wrap the wire around the core twice, and you see double the voltage. Wrap it 100x, and you see 100x the voltage. The secondary coils of step up transformers are essentially “sampling” a single circular voltage many times, and since all the “turns” of the spiral wire are connected in series, the voltages add up.
The core is made of a ferromagnetic material and both the primary and the secondary coils are wrapped around it. So, in the ideal case in wich there is no leakage, all the flux generated by the primary coil is used by the secondary to build a voltage across its terminals.
Sérgio, you missed the question. Yes, in the ideal case, all the flux passes through the core around which the secondary is wrapped. However, to produce a voltage, the flux must CUT the lines of the conductor. If all the flux is contained inside the core, then it can’t possibly cut the coil. bbeaty’s explanation sounds reasonable, but it isn’t sitting well with me. What exactly do you mean by a voltage field? - presumably a range of voltage values that exist around the core. But isn’t voltage a scalar quantity that arises from the electric field? By extension, wouldn’t the correct thing to say be that it creates an electric field, instead?
You are making a confusion. The wire does not have to cut the flux lines. All you need is that the flux passing through the coil is varying. In that case there arises a voltage that is equal to the derivative of the flux.
I think the confusion is because you are thinking of a DC generator. In this device, the flux is constant, so you must move angularly your coil across the field in order to have a variation.
Dear sir,
analogy of either cutting Flux line by conductor OR Rate change of flux linkage looks sound as far as we discuss induce emf in a loop of wire. Dear Mr. Bbeaty how would you explain emf= Blv volts induced in single straight conductor of length l, moving perpendicular to flux lines at velocity v.
Also i would like to understand emf induced in dynamo where magnet is being rotated just beside the coil.
what i mean is when a single straight conductor moves perpendicular to magnetic field of constant flux density, how flux linkage change/voltage field coupling with the conductor can be explained ?
I think this is right. Transformers don’t need to move the coil windings across magnertc flux lines. They merely vary the flux by changing the current in the primary winding.
You could cast even transformers in terms of field lines cutting conductors. As you increase the field strength, new field line loops will be created (initially with zero size) at the edges of the cylinder, and expand until they come out the ends of the cylinder, crossing over conductors in the process. You absolutely cannot avoid “leakage flux”, because magnetic field lines are always closed loops.
However, just because you can describe it this way, doesn’t mean that you should. All it does is make things more complicated and harder to understand.
I don’t understand. The core is a donut shape. There’s no way, topologically, to start with a loop of zero size and expand it to go around the donut while still being constrained within (not without a discontinuity, at least). Unless, I guess, you’re positing that the loops are created outside the core and once they’ve been stretched enough, they cut the conductors and enter the core.
Oh, I was assuming a cylindrical core. Hmm, not sure how such an interpretation would work with a toroidal core, though there might still be some way to cobble it together.
The posts above yours were made in 2004. The people who posted them are probably not still around to answer. (Someone else might answer you, though. Not me. I don’t understand it either.)
I also don’t understand Chronos’ interpretation. In fact, you can shield the toroid (or equivalently a very long solenoid) with superconductors to guarantee that no flux leaks out, and the emf is still created. In fact, this is the basis of one of the standard Aharanov Bohm experiments that show that in the quantum mechanical case, there are physical effects that occur in a region of space that is totally free of the classical force fields (though not free of both the scalar and vector potentials).
My apologies, I had a brain glitch and completely agree with your first two sentences. A superconducting shield wound around the solenoid or toroid will completely eliminate the induced EMF in the secondary. However, I still contend that the leakage flux is not necessary to explain the effect. This is true of either the infinite solenoid or the toroid, but is best illustrated with the toroid, since we avoid the issue of flux return at infinity. Imagine such a toroidal coil made with superconducting wire, with infinitesimal gaps between the turns. Flux cannot penetrate the superconducting wire and all the flux is perfectly confined within the center of the torus. Now wind a single loop through the doughnut hole. This secondary will never see any magnetic flux, even when the the current in the primary is changing; but there will be an EMF in the secondary given by the time derivative of the flux confined within the torus.
This is all straightforward classical E & M. The amazing quantum mechanical fact is that you can measure the flux within the torus (modulo the flux quantum), even with static fields in which there is never any magnetic, nor electric field anywhere outside the torus. This is the Aharanov Bohm effect. Why didn’t those guys ever win the Nobel Prize?
