at 11:02, the gradient you see is the charge density gradient. The charge distribution is the result of e-field produced by the changing magnetic field. But the charge distribution itself also produces a opposing electric-field along the wire. There are two electric fields of different origins, and the total electric field along the wire is zero. It has to be zero, because any non-zero resultant electric field will re-adjust the charge distribution until the nett e-field is zero, because a conductor by its property will have the charges moved easily by any non-zero e-field. Imagine that you are a little electron in that path, you can move along the wire without any opposing force, hence the voltage along the wire, from one terminal to another is zero. But across the gap, the voltage is non-zero.
You are correct. It's interesting that Bob claims (11:36 onwards) that he measures a voltage gradient along the wire segment which doesn't encircle the solenoid. He does this in spite of citing Romer's paper which specifically states there can be no observable induction around a closed path in what Romer designates as region II (where the curl of E is zero). Unlike Romer's experiment which employs a very long tightly pitched solenoid, Bob uses the short coil from a solenoid actuator from which he has removed the armature - leaving just the yoke and winding. It's obvious his closed path which is formed by the wire segment and the CRO measurement path must be enclosing time-varying magnetic flux flaring out from the coil - thereby giving him an indication which he is misled into thinking is a voltage gradient along the wire. He seems not to understand that his setup forms a closed circuit path or that his coil is vastly different to Romer's very long tightly pitched solenoid. I have done experiments with coils which spray flux all over the surrounding region and I understand how Bob has been fooled by his result. Of course, he depends on these results to postulate that the seat of EMF in a toroidal inductor is entirely confined to the toroidal core window, which is nonsense. Accepting that his results with his solenoid are due to an uncontained B field, would basically invalidate his claim about the toroidal case. He is probably unlikely to entertain the alternative (albeit correct) explanation. Romer considered trying to identify or postulate the seat of EMF as a pointless pursuit. In reality the so-called seat of EMF is an unobservable entity.
With EMF being directly proportionate to the rate of change in magnetic flux and the change in that flux being confined to the toroid, it makes sense that the EMF would also be confined to the toroid.
The EMF is not concentrated in the core of the center of the toroid. If you had a gapped toroid so that you could actually place wires into center so that they remain orthogonal to the magnetic field lines, then you could repeat the experiments where the potential is measured along the winding just like the previous examples. The problem is that the toroid is solid so it prevents you from having the same configuration as some of the other sundail type of experiments. Part of the problem is do we define the EMF as a property of the loop or not. If we define voltage as the integral of the electric field within the conductor, then we are forced to conclude that the EMF is a property of each loop. But if you do this, then you are basically not satisfying the KVL anymore as the right hand side of the sum of voltages (integrals of the electric field) is not zero. However, the electric field within the conductor is zero because the charges were able to move to equilibriate with the magnetic vector potential that is caused by the changing magnetic field. This causes charges to accumulate along the surfaces of the conductor such that the vector potential is exactly cancelled. That is that conductor acts to integrate the vector potential along its path. This gives rise to a different kind of potential change along the conductor, one that solves the scalar potential equation. But this point of view takes a different interpretation to what a potential difference is between two points in the circuit. The scalar potential increases uniformly along the conductors (including the probe leads of the circuit) so you cannot associate the EMF with just the action of the changing magnetic field on the segment of the conductor in the center of the toroid: It happens throughout the path. I have simulated similar circumstances and shown how these different fields behave where the conductor has a zero electric field but will have a smooth gradient of the scalar potential along it. You can see the simulations and discussions of how they relate to lumped model approximations in my video th-cam.com/video/fi7QL1TnRw0/w-d-xo.htmlsi=dLn74BXDwsAaZ3hZ I hope you find it helpful in understanding what is going on.
Toroidal cores concentrate magnetic flux within the toroid. Other inductors / transformers waste magnetic flux into free air., reducing efficiency and causing magnetic interference with other inductors / transformers.
Toroidal cores are fascinating. They are 'self shielding' with respect to near field losses. I'm no physicist but have the opinion that the magnetic field is trapped within the core because there is no finite N/S pole location because there's no 'end' of the core. The core is continuous.
One can argue the same condition is true in the case of a typical transformer. Other than leakage flux, the magnetic field is predominantly confined to the core magnetic material. This is confirmation of one of Maxwell's equations which for quasi-static conditions, states that the divergence of a magnetic field is zero. This must be true of a permanent magnet when we consider the entirety of space occupied by the magnet. When the magnetic field varies with time there will always be an electromagnetic field external to the toroidal magnetic core which (depending on the frequency of the inducing current) might appear in part as observable radiation propagating away from the core. Whilst primarily more of academic interest the helical wound toroidal antenna is an example of a radiating source. Many people are unaware of the fact that whilst the magnetic field outside the core of an ideal toroidal inductance is negligible, there exists an electric field which is the physical entity giving rise to induced current flow in a closed secondary winding wrapped around the same core.
In this video Bob considers the case of an open conductor loop wrapped around a solenoid winding carrying a time-varying electric current. The time-varying solenoid current gives rise to the time-varying magnetic field. When Bob tells us that there is a voltage gradient along the open loop he seems to be saying this is due solely to the distributed EMF. He also seems to suggest that the EMF pushes the unbound conductor charges towards one end of the open loop leaving exposed bound charge at the opposite loop end. The only possible candidate for charge redistribution along the wire is an electric field causing a motive force on unbound charges. We might then postulate some equivalence between the EMF and the electric field causing the surface charge redistribution along the wire. This is the gist of Faraday's law. The charge difference at the loop end points is apparently what gives rise to the non-zero indication of a high resistance voltmeter connected across the loop end points. If the EMF persists unopposed along the loop, the question arises as to “why doesn't the charge accumulation continue in an unbounded manner?” It seems that in Bob's mind, nothing opposes the EMF. But clearly something is limiting the charge accumulation so that an equilibrium (vis-a-vis the induced EMF) is established at any instant at any location along the loop. Bob has apparently forgotten the fact that there will be an electric field set up between the unbound and bound surface charges due to their physical separation. This electric field must be the mechanism for limiting the charge redistribution, i.e. by establishing a countering electric field to the primary electric field ‘causing’ the charges to migrate to the wire loop surface. When the fields are thus counterbalanced, there can be no resultant longitudinal electric field in the open conductor and by simple deduction, no voltage gradient can exist along the conductor. There is also a resultant electric field which exists in the region between the loop end points. This must again be attributed to the surface charge redistribution along the open wire loop. This gap electric field is non-zero, by virtue of there being very little primary EMF component (induced E field) across the gap proper. The line integral of this resultant field in the gap space accords with the non-zero reading observed on the aforementioned voltmeter connected across the loop end points.
A good reference on the topic is an answer to a question posted on Quora, viz. “How do toroidal transformers with outer secondary coils work, if no magnetic flux extends outside of the primary coil?” The answer by Roy McCammon is pretty much on the money. I've not included a link as TH-cam may reject the post. Just use the above question wording as the search term.
There should be a voltage gradient along the wire that is inside the thoroid, say if you move the leads of the voltmeter 1mm inside the thoroid, then 2 mm, then 3 mm, say for a thoroid that is 7 mm wide?
If there was any voltage gradient along the open loop wire one would expect unbound charges (electrons) to continue to migrate along the wire under the influence of the electric field giving rise to that voltage gradient. This would necessitate that charges would accumulate in an unbounded manner at the wire end points of the open loop. Such an unbounded accumulation of charges would lead to an ever increasing voltage difference across the open gap which is not observed in practice. So there can't be any steady state voltage gradient along the wire of an open loop co-located with a time-varying magnetic field.
Imagine we have a very long ‘air-cored’ solenoid winding with circular cross section. Suppose the winding diameter D is very much less than the overall solenoid length L - say L:D=50:1. A long insulated copper wire “Slinky” comes to mind. If we energised this solenoid winding with a time-varying electric current there would be a uniform tangential induced field along any circular path concentric with the longitudinal axis. This would account for the presence of a non-localised Faraday induced EMF distributed along such a closed concentric circular path external to the solenoid boundary. For a tightly pitched winding there would be negligible magnetic field external to the solenoid boundary - particularly near the longitudinal centre point, where we might place a single turn secondary loop to observe / measure a case of Faraday induction. One might reasonably ask, “How does Faraday induction arise in the external region in the effective absence of any magnetic field?”. Something to carefully ponder. Imagine now the energised Slinky solenoid ends brought together to form a circular loop of toroidal shape. Would the electromagnetic induction in the aforementioned secondary loop now suddenly have a highly localised seat of EMF, simply because of this geometrical reconfiguration? There would be a change in the induction distribution along that secondary loop, but the variation would be quite subtle. For even greater L:D ratios (e.g 75:1) the toroidal geometry would be reminiscent of an inflated bicycle tyre inner tube. The secondary loop induction distribution in that toroidal geometry case would approach that of the long straight solenoid case.
The wire passing through the core of the toroid top to bottom is the first turn of the secondary of a transformer. It does not have to loop around to count as the first turn of the secondary.
At time 13:08 you measure what you claim is a voltage gradient along the open loop segment. The loop does not enclose the solenoid, so it would not be enclosing what Romer denotes in his paper as region I. As you point out, Romer correctly asserts that a closed loop in his region II would not experience any induced emf, since the E field in region II is ostensibly curl free. To verify this claim Romer would have to guarantee that a closed loop segment incorporating a voltmeter would not give any discernible emf - i.e only if the incorporated voltmeter indicated a zero value. In your measurement along the open loop segment you have created a closed loop which incorporates a voltmeter (the CRO & probe leads) and this loop lies in what you would presumably claim is the same as Romer’s region II. Contrary to what Romer would expect you obtain a non-zero indication on your CRO. This is a contradiction of Romer's claim, unless your solenoid (unlike Romer's) spreads its magnetic flux into region II. Sure, you get a bigger indication when you close the loop with the CRO leads on the other side, but all you're really doing is making a bigger loop area which encloses more of the time-varying flux. Consider again your claim about the voltage gradient along the partial loop. As you moved your red test probe along the wire path towards the common black lead, the loop area was presumably decreasing - meaning a progressively lower induced voltage in the closed measurement loop. Your experiment does not confirm a potential gradient along the open loop segment. Romer used a solenoid winding of 444 turns over a metre in length. Even with this solenoid, Romer took special precautions to ensure his CRO measurement loop did not enclose any residual flux outside the solenoid boundary. See the last paragraph of section V in his paper. Redo the experiment with a solenoid similar to Romer's and you will get an entirely different result.
If you do a search for N. J. Carron's AJP paper "On the fields of a torus and the role of the vector potential" you have one of the best discussions of the topic. The maths is complex but the answer to Bob's question can be resolved. The induction is not confined to the core window.
I don't think your explanation is correct with the toroidal coil. Your lead wires to the voltmeter makes the loop around the magnetic field even the original loop has the ends open. No matter what you do, as long as you close the loop at the voltmeter you have induced voltage in that loop.
Do you mean "electromotive force" or EMF? The term "electromotive force" was first coined in the early 1800's by Alessandro Volta. He was mystified by the outcome of his experimental observation that dissimilar metallic junctions (along with their variation in electrolytic solutions) could give rise to continuous current flow. In the absence of current flow he could detect a potential difference (PD) across such a dissimilar metal junction with an electro-scope. He concluded that the apparently persistent electrostatic charge redistribution which gave rise to the equally persistent PD, was attributable to an underlying electromotive force. Many physicists and engineers have advocated for ridding ourselves of the term emf, which has been the subject of endless debate and conjecture. How could a physical entity with the unit of the Volt be a force? Regarding voltage. As any advanced text on Electromagnetic theory notes, voltage (or electric tension) has a widely accepted definition in terms of electric field strength. As a final comment regarding emf, one particular journal paper on the topic (by Varney & Fisher) notes “.. in each case where the term emf is used it constitutes a measure of a particular kind of non-electrostatic action on charges.” Faraday induction is a good example among many.
Voltage is an informal term, for anything measured in volts. Engineers and electricians use this term, but physicists use a term that is more accurate to what it is, rather than a conjugation of its unit name. EMF is the more general term, electric potential is a special case of EMF. EMF is the line integral of an electric field. In other words, it is the work done by the electric field, as a positive unit test charge moves between two points of interest. It could be between two different points, or it could be a closed path line integral that returns the charge to its origin. In the special case of purely electrostatic fields, the electric field is conservative, and the closed loop line integral is therefore zero. In other words, this is an electric field that is exclusively due to the positions, amounts, and signs of the charges that set up the fields, and not due to any magnetic effects. Because of this special case of the electric field, there is a concept coined called electric potential, that is used as a shortcut for evaluating the work done by the electric field. The work done moving a charge between two points, is independent of the path, and would add up to zero, returning to the same original point. This is what you get in a circuit created by batteries and photovoltaics as the energy source. A conservative electric field throughout the circuit, where the closed loop total work done on a charge as it takes a closed path, is zero. The voltage source does positive work on it, and the loads do negative work on it. Magnetic induction makes electric potential no longer a useful concept. Instead, the more general case of EMF needs to apply. Magnetic induction introduces a non-conservative field, where the closed-loop work done on a charge, is path-dependent.
If you read the paper by Robert Romer mentioned by Bob you certainly gain the understanding that there are different voltages observed on the two voltmeters connected to the same nodes. Romer correctly defines the voltage between two points as the line integral of the electric field encountered in a traversal of the particular path chosen between the two points. That's the reality of making voltage measurements in the presence of time-varying fields.
I have just had a look at Walter Lewin's video and I find that his deductions are kuku. He claims that a coils with zero resistance has no EMF. If one measures the dc resistance of a transformer it is always lower than it's impedance. A magnetic change influences the electrons in the wire regardless of the resistance in the wire. A zero resistance wire will probably even perform better than one with resistance. I believe cobber or silver is better than say aluminium. Kirchhoff's voltage law is for DC only. Your loop example is pretty much the same as a transformer where the secondary has two connections. The difference is that there are so many windings that the probe winding is insignificant. The measurement on the toroidal transformer has a closed loop outside the transformer made up of the probes and the wire. If you had more windings and went to the centre you would find that you would get the correct voltage on both sides. The wires you measure must only go one way to get a voltage. The EMF doesn't care if it is a winding wire or a sense wire. To get an answer to your last question then put in two loops. One will have the reverse EMF but not the other.
It is sometimes a convenient mathematical strategy to define an EMF along all or part of an energised transformer winding or some other device incorporating electromagnetic induction. I have adopted this myself on occasion for other situations and read journal papers taking a similar approach. However, this might lead us into puzzling conundrums or conclusions which seem contrary to established electromagnetic theory. We have to approach the idea with caution. Suppose we have an energised AC transformer with an unloaded secondary winding. We connect an oscilloscope to the secondary terminals and observe an AC waveform of a particular peak-to peak value at the AC operating frequency. The combination of the oscilloscope vertical input channel electronics plus the connected measurement leads is measuring something. From established electromagnetic theory we know that what is measured can be equated to the line integral of the electric field between the secondary terminals which exists along the total measurement path in the free space outside the transformer body. Provided there is no time-varying magnetic flux leaking out of the transformer body into the surrounding space, we can be confident that no matter where we place the oscilloscope, or along what path we route the measurement leads, we will get the same result. The electric field external to the transformer observed in the connection to the secondary terminals is conservative and the observation is independent of the measurement path adopted. We would also be confident that we could relate our CRO observation to the unloaded transformer secondary EMF, since the CRO would draw negligible load current from the transformer. Suppose now we ask what is the electric field in the actual secondary winding? Surely if we were able to take the line integral of the electric field encountered in a traversal of the winding itself between the secondary terminals, we would presumably get the same result. This must be the transformer EMF. We also know from the constitutive relationship for material media we call Ohm’s Law, that at low frequencies the electric field in a conductor carrying an electric current is given by the product of the current density and the conductor material resistivity. The copper wire used to form the transformer winding would have very low resistivity. So even if a modest current was flowing in the secondary winding, the resultant electric field along the winding would be negligible. In an unloaded secondary winding of the energised transformer there must be zero resultant electric field along the winding. Taking the line integral of the electric field along the entire unloaded winding means we have a result of zero. Oh dear, the transformer secondary has zero EMF! But we’ve fallen into a trap. If a source of EMF exists somewhere in a simple single loop circuit topology, it can only be defined if we take the line integral of the electric field encountered in a complete traversal of a closed path which includes that source of EMF. That path can include free space. If we take the line integral of the electric field encountered along the transformer winding AND the electric field encountered in a traversal of any external path in the space between the secondary terminals, we arrive at the secondary EMF. As any transformer designer worth his salt knows, the resultant electric field along an open winding of an energised transformer is zero. Whatever claims we make about the interpretation of the line integral of the electric along the winding itself are meaningless conjectures, since that entity (physical or otherwise) is not open to observation. Someone will say it’s a zero voltage - another will say it’s the EMF masked by the electrostatic field potential caused by charge redistribution along the unloaded winding. Take your pick.
See en.wikipedia.org/wiki/Toroidal_inductors_and_transformers Under heading: Toroidal transformer Poynting vector coupling from primary to secondary in the presence of total B field confinement
There is no "emf confined inside the coil". You really, really, really cannot understand nonconservative fields. All you need to worry about (in these quasistatic non-motional settings) is if your measuring loop (probes + voltmeter + portion of circuit) does not contain a changing magnetic field. If it doesn't, you are measuring the correct voltage; if otoh it does, you need to subtract the induced voltage. It's that simple. The reason you cannot find any literature to support your 'theory' is because it is wrong. Solve Maxwell's equations, along with the constitutive equation and the continuity equation and you will find out.
@@keylanoslokj1806 No modification whatsoever is needed. You can read about the correct physics in Purcell, Zahn, Geraint Rosser, Haus and Melcher, Ramo Whinnery Van Duzer, and many other respected uni level EM books.
Perhaps one of the most learned Electrical Engineers was the American Joseph Slepian. He rose to prominence in the early to mid 20th century as a designer and researcher. He eventually headed up Westinghouse Research Laboratories. Among Westinghouse's products were power transformers. Slepian understood electromagnetic theory very well and was a great advocate for educating the best and brightest in the art. Slepian would have regarded much (if not all) of this video as nonsense. When I did my undergraduate course in Electrical Engineering in the 1970's I was required to undertake studies in electromagnetic theory which included Maxwell's equations. It took many years for the theory to sink in. When Bob says let's consider a battery, you know this isn't going to advance our understanding of the topic at hand.
at 11:02, the gradient you see is the charge density gradient. The charge distribution is the result of e-field produced by the changing magnetic field. But the charge distribution itself also produces a opposing electric-field along the wire. There are two electric fields of different origins, and the total electric field along the wire is zero. It has to be zero, because any non-zero resultant electric field will re-adjust the charge distribution until the nett e-field is zero, because a conductor by its property will have the charges moved easily by any non-zero e-field. Imagine that you are a little electron in that path, you can move along the wire without any opposing force, hence the voltage along the wire, from one terminal to another is zero. But across the gap, the voltage is non-zero.
You are correct. It's interesting that Bob claims (11:36 onwards) that he measures a voltage gradient along the wire segment which doesn't encircle the solenoid. He does this in spite of citing Romer's paper which specifically states there can be no observable induction around a closed path in what Romer designates as region II (where the curl of E is zero). Unlike Romer's experiment which employs a very long tightly pitched solenoid, Bob uses the short coil from a solenoid actuator from which he has removed the armature - leaving just the yoke and winding. It's obvious his closed path which is formed by the wire segment and the CRO measurement path must be enclosing time-varying magnetic flux flaring out from the coil - thereby giving him an indication which he is misled into thinking is a voltage gradient along the wire. He seems not to understand that his setup forms a closed circuit path or that his coil is vastly different to Romer's very long tightly pitched solenoid.
I have done experiments with coils which spray flux all over the surrounding region and I understand how Bob has been fooled by his result. Of course, he depends on these results to postulate that the seat of EMF in a toroidal inductor is entirely confined to the toroidal core window, which is nonsense. Accepting that his results with his solenoid are due to an uncontained B field, would basically invalidate his claim about the toroidal case. He is probably unlikely to entertain the alternative (albeit correct) explanation. Romer considered trying to identify or postulate the seat of EMF as a pointless pursuit. In reality the so-called seat of EMF is an unobservable entity.
With EMF being directly proportionate to the rate of change in magnetic flux and the change in that flux being confined to the toroid, it makes sense that the EMF would also be confined to the toroid.
The EMF is not concentrated in the core of the center of the toroid. If you had a gapped toroid so that you could actually place wires into center so that they remain orthogonal to the magnetic field lines, then you could repeat the experiments where the potential is measured along the winding just like the previous examples. The problem is that the toroid is solid so it prevents you from having the same configuration as some of the other sundail type of experiments. Part of the problem is do we define the EMF as a property of the loop or not. If we define voltage as the integral of the electric field within the conductor, then we are forced to conclude that the EMF is a property of each loop. But if you do this, then you are basically not satisfying the KVL anymore as the right hand side of the sum of voltages (integrals of the electric field) is not zero. However, the electric field within the conductor is zero because the charges were able to move to equilibriate with the magnetic vector potential that is caused by the changing magnetic field. This causes charges to accumulate along the surfaces of the conductor such that the vector potential is exactly cancelled. That is that conductor acts to integrate the vector potential along its path. This gives rise to a different kind of potential change along the conductor, one that solves the scalar potential equation. But this point of view takes a different interpretation to what a potential difference is between two points in the circuit. The scalar potential increases uniformly along the conductors (including the probe leads of the circuit) so you cannot associate the EMF with just the action of the changing magnetic field on the segment of the conductor in the center of the toroid: It happens throughout the path. I have simulated similar circumstances and shown how these different fields behave where the conductor has a zero electric field but will have a smooth gradient of the scalar potential along it. You can see the simulations and discussions of how they relate to lumped model approximations in my video th-cam.com/video/fi7QL1TnRw0/w-d-xo.htmlsi=dLn74BXDwsAaZ3hZ I hope you find it helpful in understanding what is going on.
Toroidal cores concentrate magnetic flux within the toroid. Other inductors / transformers waste magnetic flux into free air., reducing efficiency and causing magnetic interference with other inductors / transformers.
Toroidal cores are fascinating. They are 'self shielding' with respect to near field losses. I'm no physicist but have the opinion that the magnetic field is trapped within the core because there is no finite N/S pole location because there's no 'end' of the core. The core is continuous.
One can argue the same condition is true in the case of a typical transformer. Other than leakage flux, the magnetic field is predominantly confined to the core magnetic material.
This is confirmation of one of Maxwell's equations which for quasi-static conditions, states that the divergence of a magnetic field is zero. This must be true of a permanent magnet when we consider the entirety of space occupied by the magnet.
When the magnetic field varies with time there will always be an electromagnetic field external to the toroidal magnetic core which (depending on the frequency of the inducing current) might appear in part as observable radiation propagating away from the core. Whilst primarily more of academic interest the helical wound toroidal antenna is an example of a radiating source.
Many people are unaware of the fact that whilst the magnetic field outside the core of an ideal toroidal inductance is negligible, there exists an electric field which is the physical entity giving rise to induced current flow in a closed secondary winding wrapped around the same core.
In this video Bob considers the case of an open conductor loop wrapped around a solenoid winding carrying a time-varying electric current. The time-varying solenoid current gives rise to the time-varying magnetic field. When Bob tells us that there is a voltage gradient along the open loop he seems to be saying this is due solely to the distributed EMF. He also seems to suggest that the EMF pushes the unbound conductor charges towards one end of the open loop leaving exposed bound charge at the opposite loop end. The only possible candidate for charge redistribution along the wire is an electric field causing a motive force on unbound charges. We might then postulate some equivalence between the EMF and the electric field causing the surface charge redistribution along the wire. This is the gist of Faraday's law. The charge difference at the loop end points is apparently what gives rise to the non-zero indication of a high resistance voltmeter connected across the loop end points. If the EMF persists unopposed along the loop, the question arises as to “why doesn't the charge accumulation continue in an unbounded manner?” It seems that in Bob's mind, nothing opposes the EMF. But clearly something is limiting the charge accumulation so that an equilibrium (vis-a-vis the induced EMF) is established at any instant at any location along the loop. Bob has apparently forgotten the fact that there will be an electric field set up between the unbound and bound surface charges due to their physical separation. This electric field must be the mechanism for limiting the charge redistribution, i.e. by establishing a countering electric field to the primary electric field ‘causing’ the charges to migrate to the wire loop surface. When the fields are thus counterbalanced, there can be no resultant longitudinal electric field in the open conductor and by simple deduction, no voltage gradient can exist along the conductor. There is also a resultant electric field which exists in the region between the loop end points. This must again be attributed to the surface charge redistribution along the open wire loop. This gap electric field is non-zero, by virtue of there being very little primary EMF component (induced E field) across the gap proper. The line integral of this resultant field in the gap space accords with the non-zero reading observed on the aforementioned voltmeter connected across the loop end points.
very intriguing,
it easy to believe all the emf is generated inside the coil the hard thing is how to prove (measure) it.
A good reference on the topic is an answer to a question posted on Quora, viz. “How do toroidal transformers with outer secondary coils work, if no magnetic flux extends outside of the primary coil?”
The answer by Roy McCammon is pretty much on the money.
I've not included a link as TH-cam may reject the post. Just use the above question wording as the search term.
There should be a voltage gradient along the wire that is inside the thoroid, say if you move the leads of the voltmeter 1mm inside the thoroid, then 2 mm, then 3 mm, say for a thoroid that is 7 mm wide?
If there was any voltage gradient along the open loop wire one would expect unbound charges (electrons) to continue to migrate along the wire under the influence of the electric field giving rise to that voltage gradient. This would necessitate that charges would accumulate in an unbounded manner at the wire end points of the open loop. Such an unbounded accumulation of charges would lead to an ever increasing voltage difference across the open gap which is not observed in practice. So there can't be any steady state voltage gradient along the wire of an open loop co-located with a time-varying magnetic field.
Imagine we have a very long ‘air-cored’ solenoid winding with circular cross section. Suppose the winding diameter D is very much less than the overall solenoid length L - say L:D=50:1. A long insulated copper wire “Slinky” comes to mind.
If we energised this solenoid winding with a time-varying electric current there would be a uniform tangential induced field along any circular path concentric with the longitudinal axis. This would account for the presence of a non-localised Faraday induced EMF distributed along such a closed concentric circular path external to the solenoid boundary. For a tightly pitched winding there would be negligible magnetic field external to the solenoid boundary - particularly near the longitudinal centre point, where we might place a single turn secondary loop to observe / measure a case of Faraday induction. One might reasonably ask, “How does Faraday induction arise in the external region in the effective absence of any magnetic field?”. Something to carefully ponder.
Imagine now the energised Slinky solenoid ends brought together to form a circular loop of toroidal shape. Would the electromagnetic induction in the aforementioned secondary loop now suddenly have a highly localised seat of EMF, simply because of this geometrical reconfiguration? There would be a change in the induction distribution along that secondary loop, but the variation would be quite subtle. For even greater L:D ratios (e.g 75:1) the toroidal geometry would be reminiscent of an inflated bicycle tyre inner tube. The secondary loop induction distribution in that toroidal geometry case would approach that of the long straight solenoid case.
The wire passing through the core of the toroid top to bottom is the first turn of the secondary of a transformer. It does not have to loop around to count as the first turn of the secondary.
This is how science works.
At time 13:08 you measure what you claim is a voltage gradient along the open loop segment. The loop does not enclose the solenoid, so it would not be enclosing what Romer denotes in his paper as region I. As you point out, Romer correctly asserts that a closed loop in his region II would not experience any induced emf, since the E field in region II is ostensibly curl free. To verify this claim Romer would have to guarantee that a closed loop segment incorporating a voltmeter would not give any discernible emf - i.e only if the incorporated voltmeter indicated a zero value. In your measurement along the open loop segment you have created a closed loop which incorporates a voltmeter (the CRO & probe leads) and this loop lies in what you would presumably claim is the same as Romer’s region II. Contrary to what Romer would expect you obtain a non-zero indication on your CRO. This is a contradiction of Romer's claim, unless your solenoid (unlike Romer's) spreads its magnetic flux into region II. Sure, you get a bigger indication when you close the loop with the CRO leads on the other side, but all you're really doing is making a bigger loop area which encloses more of the time-varying flux. Consider again your claim about the voltage gradient along the partial loop. As you moved your red test probe along the wire path towards the common black lead, the loop area was presumably decreasing - meaning a progressively lower induced voltage in the closed measurement loop. Your experiment does not confirm a potential gradient along the open loop segment. Romer used a solenoid winding of 444 turns over a metre in length. Even with this solenoid, Romer took special precautions to ensure his CRO measurement loop did not enclose any residual flux outside the solenoid boundary. See the last paragraph of section V in his paper. Redo the experiment with a solenoid similar to Romer's and you will get an entirely different result.
Don't tokamak fusion reactors use this principle to contain plasma? Perhaps papers related to that field would cover the physics of this.
If you do a search for N. J. Carron's AJP paper "On the fields of a torus and the role of the vector potential" you have one of the best discussions of the topic. The maths is complex but the answer to Bob's question can be resolved. The induction is not confined to the core window.
I don't think your explanation is correct with the toroidal coil. Your lead wires to the voltmeter makes the loop around the magnetic field even the original loop has the ends open. No matter what you do, as long as you close the loop at the voltmeter you have induced voltage in that loop.
Sir plz give me intuition for emf amd voltage
Do you mean "electromotive force" or EMF?
The term "electromotive force" was first coined in the early 1800's by Alessandro Volta. He was mystified by the outcome of his experimental observation that dissimilar metallic junctions (along with their variation in electrolytic solutions) could give rise to continuous current flow. In the absence of current flow he could detect a potential difference (PD) across such a dissimilar metal junction with an electro-scope. He concluded that the apparently persistent electrostatic charge redistribution which gave rise to the equally persistent PD, was attributable to an underlying electromotive force.
Many physicists and engineers have advocated for ridding ourselves of the term emf, which has been the subject of endless debate and conjecture. How could a physical entity with the unit of the Volt be a force?
Regarding voltage. As any advanced text on Electromagnetic theory notes, voltage (or electric tension) has a widely accepted definition in terms of electric field strength.
As a final comment regarding emf, one particular journal paper on the topic (by Varney & Fisher) notes “.. in each case where the term emf is used it constitutes a measure of a particular kind of non-electrostatic action on charges.” Faraday induction is a good example among many.
Voltage is an informal term, for anything measured in volts. Engineers and electricians use this term, but physicists use a term that is more accurate to what it is, rather than a conjugation of its unit name.
EMF is the more general term, electric potential is a special case of EMF.
EMF is the line integral of an electric field. In other words, it is the work done by the electric field, as a positive unit test charge moves between two points of interest. It could be between two different points, or it could be a closed path line integral that returns the charge to its origin.
In the special case of purely electrostatic fields, the electric field is conservative, and the closed loop line integral is therefore zero. In other words, this is an electric field that is exclusively due to the positions, amounts, and signs of the charges that set up the fields, and not due to any magnetic effects. Because of this special case of the electric field, there is a concept coined called electric potential, that is used as a shortcut for evaluating the work done by the electric field. The work done moving a charge between two points, is independent of the path, and would add up to zero, returning to the same original point.
This is what you get in a circuit created by batteries and photovoltaics as the energy source. A conservative electric field throughout the circuit, where the closed loop total work done on a charge as it takes a closed path, is zero. The voltage source does positive work on it, and the loads do negative work on it.
Magnetic induction makes electric potential no longer a useful concept. Instead, the more general case of EMF needs to apply. Magnetic induction introduces a non-conservative field, where the closed-loop work done on a charge, is path-dependent.
Like you said in previous videos, Bob...There is no difference in voltage, if your probes are measuring from the same point in a circuit.
If you read the paper by Robert Romer mentioned by Bob you certainly gain the understanding that there are different voltages observed on the two voltmeters connected to the same nodes. Romer correctly defines the voltage between two points as the line integral of the electric field encountered in a traversal of the particular path chosen between the two points. That's the reality of making voltage measurements in the presence of time-varying fields.
I have just had a look at Walter Lewin's video and I find that his deductions are kuku. He claims that a coils with zero resistance has no EMF. If one measures the dc resistance of a transformer it is always lower than it's impedance. A magnetic change influences the electrons in the wire regardless of the resistance in the wire. A zero resistance wire will probably even perform better than one with resistance. I believe cobber or silver is better than say aluminium.
Kirchhoff's voltage law is for DC only.
Your loop example is pretty much the same as a transformer where the secondary has two connections. The difference is that there are so many windings that the probe winding is insignificant.
The measurement on the toroidal transformer has a closed loop outside the transformer made up of the probes and the wire. If you had more windings and went to the centre you would find that you would get the correct voltage on both sides. The wires you measure must only go one way to get a voltage. The EMF doesn't care if it is a winding wire or a sense wire.
To get an answer to your last question then put in two loops. One will have the reverse EMF but not the other.
It is sometimes a convenient mathematical strategy to define an EMF along all or part of an energised transformer winding or some other device incorporating electromagnetic induction. I have adopted this myself on occasion for other situations and read journal papers taking a similar approach. However, this might lead us into puzzling conundrums or conclusions which seem contrary to established electromagnetic theory. We have to approach the idea with caution.
Suppose we have an energised AC transformer with an unloaded secondary winding. We connect an oscilloscope to the secondary terminals and observe an AC waveform of a particular peak-to peak value at the AC operating frequency. The combination of the oscilloscope vertical input channel electronics plus the connected measurement leads is measuring something. From established electromagnetic theory we know that what is measured can be equated to the line integral of the electric field between the secondary terminals which exists along the total measurement path in the free space outside the transformer body. Provided there is no time-varying magnetic flux leaking out of the transformer body into the surrounding space, we can be confident that no matter where we place the oscilloscope, or along what path we route the measurement leads, we will get the same result. The electric field external to the transformer observed in the connection to the secondary terminals is conservative and the observation is independent of the measurement path adopted. We would also be confident that we could relate our CRO observation to the unloaded transformer secondary EMF, since the CRO would draw negligible load current from the transformer.
Suppose now we ask what is the electric field in the actual secondary winding? Surely if we were able to take the line integral of the electric field encountered in a traversal of the winding itself between the secondary terminals, we would presumably get the same result. This must be the transformer EMF. We also know from the constitutive relationship for material media we call Ohm’s Law, that at low frequencies the electric field in a conductor carrying an electric current is given by the product of the current density and the conductor material resistivity. The copper wire used to form the transformer winding would have very low resistivity. So even if a modest current was flowing in the secondary winding, the resultant electric field along the winding would be negligible. In an unloaded secondary winding of the energised transformer there must be zero resultant electric field along the winding. Taking the line integral of the electric field along the entire unloaded winding means we have a result of zero. Oh dear, the transformer secondary has zero EMF! But we’ve fallen into a trap. If a source of EMF exists somewhere in a simple single loop circuit topology, it can only be defined if we take the line integral of the electric field encountered in a complete traversal of a closed path which includes that source of EMF. That path can include free space. If we take the line integral of the electric field encountered along the transformer winding AND the electric field encountered in a traversal of any external path in the space between the secondary terminals, we arrive at the secondary EMF. As any transformer designer worth his salt knows, the resultant electric field along an open winding of an energised transformer is zero. Whatever claims we make about the interpretation of the line integral of the electric along the winding itself are meaningless conjectures, since that entity (physical or otherwise) is not open to observation. Someone will say it’s a zero voltage - another will say it’s the EMF masked by the electrostatic field potential caused by charge redistribution along the unloaded winding. Take your pick.
See en.wikipedia.org/wiki/Toroidal_inductors_and_transformers
Under heading: Toroidal transformer Poynting vector coupling from primary to secondary in the presence of total B field confinement
There is no "emf confined inside the coil". You really, really, really cannot understand nonconservative fields.
All you need to worry about (in these quasistatic non-motional settings) is if your measuring loop (probes + voltmeter + portion of circuit) does not contain a changing magnetic field. If it doesn't, you are measuring the correct voltage; if otoh it does, you need to subtract the induced voltage. It's that simple.
The reason you cannot find any literature to support your 'theory' is because it is wrong. Solve Maxwell's equations, along with the constitutive equation and the continuity equation and you will find out.
Where have you published your own modifications of Maxwell's equations?😂
@@keylanoslokj1806 No modification whatsoever is needed. You can read about the correct physics in Purcell, Zahn, Geraint Rosser, Haus and Melcher, Ramo Whinnery Van Duzer, and many other respected uni level EM books.
@@copernicofelinis uni professors are theoreticians not engineers. Disconnected from reality
@@keylanoslokj1806 Ramo Whinnery vanDuzer is a textbook for engineers. Try to read it.
Perhaps one of the most learned Electrical Engineers was the American Joseph Slepian. He rose to prominence in the early to mid 20th century as a designer and researcher. He eventually headed up Westinghouse Research Laboratories. Among Westinghouse's products were power transformers. Slepian understood electromagnetic theory very well and was a great advocate for educating the best and brightest in the art. Slepian would have regarded much (if not all) of this video as nonsense.
When I did my undergraduate course in Electrical Engineering in the 1970's I was required to undertake studies in electromagnetic theory which included Maxwell's equations. It took many years for the theory to sink in. When Bob says let's consider a battery, you know this isn't going to advance our understanding of the topic at hand.