# Induced Emf in loop of wire

A circular loop of wire has a changing magnetic field running through it...however, the magnetic field is not touching the wire; its contained so that it simply runs through the loop without touching the wire. Apparently, there is still an emf through the wire even though the magnetic field is not touching it. Its acceptable when looking at the mathematical equations, but how does it conceptually work: the magnetic field is not even touching the wire, but its still producing an emf. How does that happen??

## Answers and Replies

Related Classical Physics News on Phys.org
The changing magnetic field causes an electric field, which propagates out and moves the charge carriers in the wire.

O_O.....oh. Thats new to me...so, technically, thats how it works. Amazing...so they cause an electric field that propogates outward and moves the charges. Thank you genneth...I've searched long and hard for an answer and at last you have provided it.

Note that the amazing thing here is the fact that the induced EMF does not depend on, say the precise shape or orientation of the wire, but only on the rate of change of flux. That is something which is not immediately obvious from the mechanical picture I gave above.

If you are familiar with Maxwell's equations (and vector calculus), the relevant equation is $$\nabla \times E + \dot B = 0$$. Considered over a finite area, you find that

$$\oint_{\partial S} E \cdot dl = - \int_{S} \dot{B}\cdot dS$$

this is the derivative question: we say that the loop me made encircled the magnetic field inside it, but from mathematical view, we can also say that the loop encircle the outer part of it (thee 'outside' of the world), this way, our original (the one that was encircled inside the loop) magnetic field is not encircled now, then what causes the EMF on the wire?

Once again, I'll probably be flamed for this, but "what causes anything" will never be fully understood. In science, we have limited ability regarding how small of a particle/wave/force/energy that we can detect.

As far as induction goes, a magnetic field H, and an electric field E, cannot exist independently under *time-varying* conditions. When a loop is in a time-varying H field, current (mmf) and voltage (emf) are induced. Also, the time-varying, herein just referred to as "ac", H field is always accompanied by a non-zero E field. Wherever there is one, the other is right there with it. Please don't ask me which is the cause or effect as I can't answer, as no one can.

What causes the emf? What causes the mmf? I don't know. Science is based on empirical observation. Induction has been observed to take place in a consistent repeatable manner. That's all we know.

@cabraham: r u trying to answer the original question? or mine?

While the magnetic flux might "flow" through a Core like in a transformer the magnetic Field does "touch" the Connector. Note that if the magnetic field is steady state, there will be current in the conductor (I presume you mean wire) only when the field is established and disestablished. The rest of the time the magnetic field does not change.

Think of a Transformer core in the shape of a square. Around one edge is a wire wrap that can be energized with an electric current. Thos will be the hot side
Around the opposite (or any other edge, but the original) you have a wire wrap attached to an amp meter. This will be the cold side.
When the hot side is energized with Direct Current, there will be a building Magnetic field created in the core. That field will act upon the electrons in the cold side causing a momentary current spike. Once the field is fully established, there will be no flux lines causing electrons to move on the cold side, thence no current flow. The the hot side is de-energized, the reverse will occur causing a reverse current spike.

Obviously, using an alternating current on the hot side, will cause the magnetic field to rise and collapse with the current allowing an Alternating Current to be creating in the cold side.

Vp/Vs = Np/Ns

Where Vp is the Applied or primary voltage and Vs is the Created or secondary Voltage.
Np is the number of turns on the primary side and Ns is the number of turns on the secondary side.
Also the amount of current increases with number of turns. The current applied would appear to not exceed the rating of the Wire, but a greater number of turns would create a greater flux and thus a greater flux, a greater output current.

Say you want to change 120 VAC at one amp into 16VAC (the voltage needed to produce 12 Volts DC after rectification and filter). What need to be the turns ratio to produce the Required output voltage? What will be the potential current output with one Amp input?

So we have a ratio of 120/16 which is 7.5 to one. or 100 to 13.3 for one amp output. Raising the Number of turns increase the out put amperage. So say 300 turns on the primary would equal 40 turns on the secondary. Neglecting losses (always fun to do!),
we would have a three amp output. and so on. The out put current is limited primarily by the Core Flux saturation and the size of the output wire.
For a 30 amp peak current, we would need 3000 turns on the primary and 400 turns on the secondary. I'll let you determine the wire sizes.
Edmund

The changing magnetic field causes an electric field, which propagates out and moves the charge carriers in the wire.
I dont get it. Say you have this core material that has the original B field inside it. Are you saying there's magnetic field outside the core also?

@cabraham: r u trying to answer the original question? or mine?
Yours. But, it's only fair that I answer the OP as well.

When a loop encircles an ac H field, there is also present a non-zero E field. One cannot exist without the other. By definition, voltage, or emf, is computed as the line integral of the E field along a particular path. For a loop encircling an ac H field, the accompanying E field has what is called "circulation", or "curl", or "rotation". The E field integrated around the closed path is non-zero, as well as the emf. The equations have already been given above.

Fields, both E and H, carry energy. Also, energy can be transferred between tham. An L-C resonant tank circuit is an example. With induction, a source generates an ac H field, as well as E. These fields propogate and impinge on the loop. Energy is transferred to this loop. If the loop is well coupled to the source of the fields, its fields due to its own induced power will induce into the source. A transformer works in this manner.

It's all about energy transfer. Does this help? BR.

Claude

K, that's the physics, but my question is : if we picture the loop to enclose the outer part where the original magnetic field in the original question doesn't seem to lie on it, how should we compute/modify the mathematical equation to show that the electric field still exists? because once again it seems that the loop doesn't enclose any magnetic field..

so basically i'm just playing around with the words 'what encircles what',

so what's ur answer?

thanks to anyone who's replying this
indr0008

K, that's the physics, but my question is : if we picture the loop to enclose the outer part where the original magnetic field in the original question doesn't seem to lie on it, how should we compute/modify the mathematical equation to show that the electric field still exists? because once again it seems that the loop doesn't enclose any magnetic field..

so basically i'm just playing around with the words 'what encircles what',

so what's ur answer?

thanks to anyone who's replying this
indr0008
Remember that B-field lines never stop --- if you have some flux through a region, there will be a return flux through the complement.

verified. thank u very much

genneth, if what you say is true about the electric fields (in loops) outside the 'core', then there must also be a magnetic field.

It simplifies things to assume some cylindrical symmetry, and where the magnetic field strength in the core, dB/dt is a triangular wave. |dB/dt| = constant

So, during a time where dB/dt is constant in the core, then the electric field magnitude is in the surrounding region is proportional to 1/r. This gives rise to an additional magnetic field--and so on and so on. Is that a Bessel function? I dunno.

After this sequence converges, the induced EMF around a circular loop would be dependent upon the distance from the core.

I'd like to know where I errored if this is wrong.

genneth, if what you say is true about the electric fields (in loops) outside the 'core', then there must also be a magnetic field.

It simplifies things to assume some cylindrical symmetry, and where the magnetic field strength in the core, dB/dt is a triangular wave. |dB/dt| = constant

So, during a time where dB/dt is constant in the core, then the electric field magnitude is in the surrounding region is proportional to 1/r. This gives rise to an additional magnetic field--and so on and so on. Is that a Bessel function? I dunno.

After this sequence converges, the induced EMF around a circular loop would be dependent upon the distance from the core.

I'd like to know where I errored if this is wrong.
I don't see what's wrong... You've essentially got an outgoing wave in a cylindrical pattern. If you really want to calculate the precise form of the fields, look up the retarded Green's functions for the vector potential.

I don't see what's wrong... You've essentially got an outgoing wave in a cylindrical pattern. If you really want to calculate the precise form of the fields, look up the retarded Green's functions for the vector potential.
well... as discribed, it's not a wave, and the transformer equation is violated.

Yeah, well, your post #2 was better than the time I asked this question, and got a resounding echo.

I deliberately setup the problem without time varying fields to avoid adding more theory. A textbook solution would be nice to see.

Can't be simpler!

No current, no field! No field. no current.!

You can't have a field with out a current. The earth's magnetic field is caused by the current of the energized magma rotating inside the mantle.

So there is an ever present magnetic field, but it is very weak compared to those generated by electric currents. and we usually ignore them because they are so minor. Wrap as much wire around a magnetic core, laminated or torrid, as you want, but if it is not cutting across magnetic lines, it will not produce a current. If you could wave it around very, very fast you might get a measurable current, but it would be minuscule. On the order of nanoamps.

You need review what causes a current and what causes an electro/magnetic field.
You responses indicate a basic lack of understanding of both!

Edmund

Note that the amazing thing here is the fact that the induced EMF does not depend on, say the precise shape or orientation of the wire, but only on the rate of change of flux. That is something which is not immediately obvious from the mechanical picture I gave above.

If you are familiar with Maxwell's equations (and vector calculus), the relevant equation is $$\nabla \times E + \dot B = 0$$. Considered over a finite area, you find that

$$\oint_{\partial S} E \cdot dl = - \int_{S} \dot{B}\cdot dS$$
Actually, the induced EMF does depend upon the shape of the inductor. The changing magnetic flux generates an electric field. The second rate change in magnetic flux generates a changing electric field exterior to the windings. The changing electric field results in an additional magnetic field. This field induces an additional electric field, and so forth, such that the EMF around a loop depends upon its shape and size.

A physical solution requires application of both Faraday's law and Ampere's law.

Last edited:
Actually, the induced EMF does depend upon the shape of the inductor. The changing magnetic flux generates an electric field. The second rate change in magnetic flux generates a changing electric field exterior to the windings. The changing electric field results in an additional magnetic field. This field induces an additional electric field, and so forth, such that the EMF around a loop depends upon its shape and size.

A physical solution requires application of both Faraday's law and Ampere's law.
Very good, Phrak. For some reason, whenever induction is discussed, many posters obsessively quote Faraday's law ad infinitum while ignoring Ampere's law. Both are equally important and both are immutable at all times under all conditions.

You are correct. The emf depends upon the shape of the inductor as well as its cross-sectional area. The line and surface integrals above demonstrate that. Peace.

Claude

Very good, Phrak. For some reason, whenever induction is discussed, many posters obsessively quote Faraday's law ad infinitum while ignoring Ampere's law. Both are equally important and both are immutable at all times under all conditions.

You are correct. The emf depends upon the shape of the inductor as well as its cross-sectional area. The line and surface integrals above demonstrate that. Peace.

Claude

Well, maybe I was unclear. As well, for a given shape and size of inductor, the induced emf around a loop depends on the loop-path.

You Are Correct Sir!

I was trying to simplify and tripped over my own example. Of course, the shape of the core does matter. A laminated torrid is more efficient in reducing Hysteresis and thus loss of magnetic field force! As opposed to a piece of iron bar.
I didn't really want to get into all that, when it appeared that more basic problems were at issue.

Last edited:
Dozent, we're all learning as we go here, it seems. Faraday's law in integral form tells you the a changing magnetic flux through an area will induce an electric field around the boundry to that area.

If you want to know what the local fields look like, you need Faraday's law expressed using a cross product. An introductory text will utilize the integral form, then introduce EMF around a loop. Notice that the EMF is independent of the loop path as long as each path surrounds the same flux.

Building upon this, the transformer equation is obtained where the path taken around the core does not enter into the equation.

But this is a minor swingle. You've been had. The transformer equation is not as general as believed. My own text slips this one by the reader by tacitly ignoring the fact that the magnetic flux cannot be contained entirely within a solenoid, no matter that it's infinitely long.

Unfortunately, the resulting equations, where both the electric and magnetic fields interact and change with time are not so simple, apparently involving things like transendental functions 'n stuff, so it becomes apparent why an introductory text might be inclined to whitewash things a bit.

Then maybe i am confused as to the purpose of this site. Granted my studies were over 35 years ago, but I thought that were we here to help students to understand basic classical concepts. Not to debate subjects that require transcendental formations, Lei algebra, or calculations of Quantum mechanics. I use heuristic models to attempt to explain TO STUDENTS what the answer to their questions could be. I have found that visual explanations are usually better than just throwing equations.
I do not participate in this site to debate physicists over esoteric variations of equations.
Edmund

Last edited:
Well, I'm a student--of sorts. But I don't get a lot of traction in that endevor here.

Your post #18 threw me off. What did you teach?