On a mailing list that I am on someone described an experiment in which they made a transformer where the primary consisted of a normal winding of insulted copper wire. The transformer was one designed to be easily disassembled for demonstrations.

They made a secondary of 15 turns of 1mm PVC insulated wire and measured the output, both open, and under load. Then they made an identical secondary except that it was encased in a ring of steel pipe with the ends not quite touching.

When the primary was powered up, the output voltage induced in the 15 turn secondary was the same whether it was unshielded or inside the ring of steel pipe. Open circuit voltage or voltage measured with a lamp load were not affected by the presence of the pipe.

The experimenters question was, if voltage induced in the secondary involves the coil cutting the flux as they referred to it, why was voltage not reduced when shielded inside the steel pipe. And a secondary question was, in a transformer design where flux is designed to stay in the core, how does it cut the coil and induce a voltage. Any flux which does escape the core is considered “leakage flux” and generally transformer cores are designed to minimize that. I’d add to that, a toroidal transformer where there is essentially no leakage flux is as efficient as you can get.

The whole cutting lines of flux concept is one I’ve never been comfortable with, I think it derives from the old iron filings experiments where they filings lined themselves up in lines that people assumed to be magnetic lines of force, but I think that assumption was incorrect; without the filings there is just a magnetic field gradient, not “lines”, the lines form because when one filing aligns with the gradient, it essentially short-circuits that magnetic field gradient over it’s length and so the magnetic gradient potential is higher near it’s ends attracting other filings, they in turn do the same thing and so the end result is filings self-organizing themselves into lines.

The questions are of interest. Working in various fields involving transmission of audio signals in shielded coaxial cables, I’ve always noted the lack of 100% effective shielding and attributed that to the fact that the shielding materials had electrical resistance and where therefore unable to completely exclude magnetic fields. I wouldn’t have been surprised that some field is induced in the secondary, after all the shield was incomplete, there was a gap, and steel is not a particularly good conductor and therefore shield.

That no difference in output was observed, that is surprising, and then the whole question about transformer theory and flux being contained within the core is also interesting. Please feel free to use comments or e-mail to add your thoughts on this subject.

The “anomaly” in this case is only in the mind of the observer. This experiment behaves exactly as predicted by Maxwell’s equations. The induced voltage along a closed path is proportional to the time derivative of the flux INTEGRAL through the loop area… which tells us that there is something inherently non-local at work, even if that non-locality happens to be expressed ALMOST completely in local equations… almost but not quite, that is. But the theory and its properly used equations do not require in any way that there is a local magnetic field at any point of the loop itself, as long as there is a flux (change) through the loop, which means ALL of the area inside the loop, not just the part close to the loop itself.

At first this might appear counterintuitive to the novice who was falsely told (or naively assumes) that electro-magnetism is a strictly local phenomenon “just like” static electric charge. It is not (as one could already have guessed form the observation that there are OPEN electric field lines but NEVER any open magnetic ones) and this makes it much more complicated and rich in surprises like this experiment shows.

If one has the time, patience and luck to study electromagnetic fields all the way through a complete physics curriculum, one can learn that electromagnetic E and B fields are the derivatives of relativistic potentials which, in a suitable gauge, can be written as a scalar potential phi and a vector potential A. A is a three-(dimensional) vector which behaves fundamentally different from the scalar field phi and this shows in every bit of the properly formulated theory as well as in virtually every experiment with magnetism. And while modern under-graduate physics books like to stress the local forms of Maxwell’s field equations (supposedly because they are more intuitive… go figure why physics needs to be “intuitive” instead of correct), this treatment cuts out almost all of the really fundamental physics that can be derived from looking at electromagnetism alone without actually getting into the underlying quantum mechanics and field theory where E and B are of secondary value and almost everything revolves around phi and A.

Interestingly enough, older theory books get it right… and probably inconvenience the casual reader too much with their endless talk of differential line-, area- and volume-elements and other “stuff” that requires familiarity with three and four dimensional integrals. None of which the casual reader will likely be familiar with because it is not properly taught in the math prep courses that lead up to the physics classes. I wasn’t taught it, either… and I can feel everyone’s pain having to learn non-trivial multi-dimensional analysis and physics at the same time…

Be that as it may, the experiment at hand can be extended very easily by measuring the electric potential difference (voltage) between the ends of the iron tube… it happens to be the same as the one per turn of the conductor on the inside… the tube, because it is not shorted, simply does not “isolate” the closed electric field lines around the flux change. Only by shorting the tube will the loop potential get shorted and a current will flow which (according to Lenz’s rule) must act against the induction field. And it is this current which will (in case of ideal conductors) completely eliminate the flux inside the loop. The result would be a completely field free toroidal space INSIDE the tube… and a shorted transformer which would catch fire fairly quickly. Which is probably one of the reasons why this essential part of the experiment is not shown…

OK… hope this helps… it won’t get me tenure at a university, but at least you get the picture… this is an absolutely great experiment which COULD be used to demonstrate some of the most amazing physics ever discovered. The PROPER mathematical explanations have enormous weight, not just for understanding a simple transformer but for almost all of physics beyond classical mechanics. These kinds of non-local effects play a role from the magnetic properties of elements to the nuclear reactions in stars, the magnetic fields that accelerate cosmic rays and even the stuff that makes up all of the universe… quarks, gluons, the Higgs boson, you name it, depends on it. All these more fundamental theories contain aspects of local field theories with non-trivial non-local effects, just like the probably easiest of all physically relevant non-trivial field theories, electromagnetism, demonstrates in this transformer experiment. And much of what we know today can already be glimpsed in those phenomena our great-great-great-grandparents discovered.

To say that a maths equation explains something may well please a mathematician, but it does not really “explain”. The fact that a voltage is induced proportional to the time derivative of the flux integral simply predicts that it works. Not WHY it works.

Maths may well predict. It does not explain the process. There is still an unknown process involved here that noone to my knowledge understands. What exactly induces the voltage? It sure aint flux! It seems that the flux changing does something, and THAT induces the voltage. What is the in-between thing?

I believe that should we discover what that process is, we may well discover a plethora of spinoffs. …antigravity perhaps? Who knows?

The experimenter in this case, was myself. It was a surprise to stumble upon this site and find this blog. Good, too, to find that others thought the issue was of interest.

Many thanks for the opportunity to comment.

RALPH DEAN

Australia

An interesting experiment is the following (Haus, H.A. and J.R. Melcher, Electromagnetic Fields and Energy): A magnetic ﬂux is created in the toroidal magnetizable core by driving the winding with a sinsuoidal current. Looped in series around the core are two resistors of unequal value, R1 and R2. Thus, the terminals of these resistors are connected together to form a pair of “nodes.” One of these nodes is grounded. The other is connected to high impedance voltmeters through two leads that follow different paths. A dualtrace oscilloscope is convenient for displaying the voltages. Voltages measured between the terminals of the resistors by connecting the nodes to the dualtrace oscilloscope, differ in magnitude and are 180 degrees out of phase (v1/v2=-R1/R2). It is the same when someone goes with a voltimeter to measure the voltage between the nodes. The results differ according to the resistence one has in front of.