Ampere's law applies indeed generally, so in the DC case the magnetic field H (inside as well as outside the wire) does not depend on the material of the wire. It might be a matter of taste but I prefer to write ∇×H = J for this reason. In other words, H depends on I while B depends on both H and μ at the location under observation.

At a certain current, the density of the magnetic flux, B, is much larger inside an iron wire (large μ) than inside a non-ferromagnetic wire but - like H - B is uneffected by the material of the wire in the air (μ = μ0) around the wire.

Hard iron could be permanently magnetized by a large enough current but the field would remain exclusively inside the wire (after the current is switched off), i.e. the wire would not attract other ferromagnetic objects in the neighborhood. As Jerry Decker suggested to another of your questions, in the context of a disk, if the wire could be split into radial segments afterwards, then the magnetization would become evident.

The iron wire will not absorb all the flux around the wire. The line integral of magnetic field around a loop is always equal to the total current through the loop. This means that outside the wire, where the field line follow circular paths because of symmetry, the magnetic field H is given by 2 pi r H = I = total current in the wire.

Then H=I/(2 pi r) and because this field is in air, the magnetic flux B is

mo H =mo I/(2 pi r). This is the same for wire of any material.

Inside the wire the flux will be higher than in copper wire, for instance, although the profile may be different (I don't know), but it will be zero in the middle and highest at the outside. If the flux distribution is different, the current distribution in the wire must be different too.

Dear Emanuel,

Interesting question. You can solve the Ampere's law equation, with B = muo. H + M. You should know the relation M(H). I think this can be solved iteratively (numerically), if the relation is nonlinear

With the relative permeability μr of copper at ~0.999 (diamagnetic) and aluminum as well as air at ~1 and for pure iron (99.8%) about ~5000 (https://www.engineeringtoolbox.com/permeability-d_1923.html) thus the magnetic reluctance:

R=L/(μ0μrΑ) (https://en.wikipedia.org/wiki/Magnetic_reluctance)

of the iron would be 5000 times smaller than that of a copper or aluminum wire and the surrounding air around the wire for a given length and thickness of the wire.

Therefore I expect in practice there will be no or negligible magnetic flux thus zero magnetic field B field created on the air around such an iron wire. The iron will confine practically all the flux inside it having a magnetic shielding effect, isolating the magnetic field on in the wire from the surrounding air. We could say that iron wires are naturally magnetically shielded.

I predict two parallel naked iron wires with the same direction large current passing through, not to be attracted or relative negligible little compared with normal copper or aluminum wires, unless in physical contact (assuming there are not naked) with each other or very small separation between them.

Inside the iron wire material the form of the magnetic flux will be indeed concentric rings with the strength of the magnetic B field in the ring formation being zero at the exact center of the wire and reaching its maximum at the surface of the naked iron wire at distance from the center r, with r=RW where RW is the given radius of the wire (i.e. thickness of wire RW not to be confused with magnetic reluctance R).

Actually it can be proven that the magnetic concentric ring B field inside any D.C. wire electric conductive material varies in strength with distance from the center of the wire by the equation attached herein (see attached equation figure) with the magnetic ring field strength reaching its maximum at the surface of the naked wire, distance from center r=RW. Where μ in this equation is the magnetic absolute permeability of the wire material. After the surface boundary of the wire is passed the field diminishes on air with distance r calculated by the equation B=μ0Ι/2πr using Ampere's Law but assuming an infinite long therefore also infinite thin wire1. This last restriction in Ampere's law of an infinite long wire so that the equation is true is necessary in order to take into account the physical phenomenon of the magnetic flux in a D.C. wire preference to concentrate on the surface of the wire and less on its bulk inner center as shown in the attached figure equation.

Especially in a soft iron wire, regarding of magnetic flux density (i.e. B field strength) in contrast to a copper or aluminum wire where these materials share the same relative permeability μr ~1 value with air, crossing the surface of the iron wire to the surrounding air will bring a dramatic reduction in the magnetic flux density since the magnetic relative permeability of soft iron is μr~5000 larger than air.

Therefore the magnetic field on air around a soft iron wire is practically nullified.

This can have interesting applications on coaxial wires whenever magnetostatic shielding is necessary in addition to EM radiation shielding where a mantle of soft iron could be applied additionally.

Also, even more natural magnetostatic shielded wires can be constructed when using mu-metal with relative permeability 80,000 to 100,000 as the wire conductor material although these wires would provide shielding for relative small currents inside them since mu-metal has a small relative magnetic saturation threshold compared to soft iron. However, mu-metal is already being used nowadays as a mantle in magnetic shielding of wires for various applications (https://en.wikipedia.org/wiki/Mu-metal). For large currents carrying wires soft iron mantle magnetic shielding would be more preferable.

For soft iron and mu-metal as the electric conductor material in wires there is of course the drawback of the reduced conductivity σ, therefore also higher ohmic resistance and heating of the wire, σ~10x106 S/m for iron and σ~1.7χ105 S/m for mu-metal compared to σ~58.7x106 S/m of copper and σ~36.9x106 of aluminium.

------------------------------

1 http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html

If we consider a very long wire (from -L to +L) of a few millimeters in diameter and made of iron (bcc-Fe; magnetized in the direction of the wire axis - y direction – “ your picture”), the magnetic induction in the plane perpendicular to the wire (point y = 0) will be in the direction perpendicular to the plane and its intensity will decrease as the measurement point moves away from the wire. On the other hand, the magnetic induction due to the current in the wire will (as shown in the drawing) be parallel to the plane.

The magnetic moment of Fe atoms can be considered to be 2.2 Bohr magnetons. With the density of bcc-Fe, the atomic mass of Fe and the approximate dimensions of the wire, it will be possible to determine the saturation magnetization of the wire and thus calculate the maximum value of magnetic induction. This result can be compared with the value of the magnetic induction associated with the current. A great didactic exercise. In particular, I think it would be very difficult to experimentally observe changes in the shape of the field produced by the current.

@Emmanouil Markoulakis

If this were true then you had successfully disproved the principle of energy conservation:

Align several straight pieces of wire along the same axis, for each piece applies length >> diameter, the material is copper and iron, in an alternating way. Connect the pieces electrically, and complete this straight piece to a closed circuit with a current source somewhere in the distance.

Take a second circuit of rectangle shape, the length of the sides less than the length of the straight pieces. This second circuit is made from copper, and is carrying a current, too. Align the second circuit in such a way that it will be attracted by the first circuit. Move the second circuit parallel to the straight section of the first circuit.

Now superpose the straight movement with another movement transversal to the first one in such a way that the second circuit approaches the first one while near one of the copper sections, and moves away while near one of the iron sections.

The approaching takes place in a strong B field, the receding in a weak one, thus you gain energy! The remaining effects (induction in the circuits etc.) add up to zero, energetically.

Probably needless to say, that is not possible.

Joerg Fricke ,

I've said B~0 not B=0 outside the soft iron wire. Try to make a solenoid using soft iron wire and then try to measure the magnetic field inside the solenoid at the center axis. You will be surprised how weak it will measure compared to the predicted value. The soft iron wire will behave as a solenoid ferromagnetic core draining most of flux out of the solenoid's air gap. Efficient solenoid's are possible when cooper or aluminium wire is used simply because the permeability of the wire is practically the same with that of air or vacuum thus ~1.

B = 0 isn't necessary. If B is weaker outside an iron wire than outside a copper wire then not only the principle of conservation of energy is violated but Newton's third law as well resp. the principle of conservation of momentum.

I feel the crucial point is the notion of "shielding". This is a fine term on the level of engineering: If I know the fields and the properties of the shielding material I can calculate the attenuation of the fields by a certain shielding box, for example.

But on a deeper level we know that the Maxwell equations do not permit attenuated fields. According to Maxwell, the only way to get a weaker field (without modifying the source) is by superposition with another field.

Exact calculations based on shielding and based on superposition yield the same results for practical purposes, but in my experience when we just visualize things the concept of shielding can lead us astray.

In the case of B outside a wire: Since we cannot change the permeability of air, to get a weaker B, we need a weaker H. To get a weaker H, we need a second field of the same shape but opposite direction as compared to the H caused by the current. How could such a H field be generated if not by a current in the wire in the opposite direction (which would result in a weaker total current)?

A solenoid is quite another matter than the straight wire in your initial picture because in a solenoid, each section of wire is crossed by the field caused by the other sections.

Most simple setup, I guess: A circular wire carrying a current and a second straight piece of soft iron wire without current, located somewhere near the first wire. Certainly there are locations where the H and B fields caused by the current are weaker than in the absence of the second wire because the second wire becomes magnetized, and the field of the second wire outside the second wire is directed, at least partially, opposite to the field caused by the current.

I agree with that. The straight piece of soft iron will be magnetized with opposite polarity at its open ends to the loop non-iron wire front and back loop areas.

I suggest do the experiment, should be easy. However, use a magnet to measure the strength of the field. such as in

Article Magnetostatics relation to gravity with experiment that reje...

My own 2 cents is that the current in a straight wire is carried on the outside surface of the wire and it is the electrons moving that product the magnetic field. Further, a solenoid has current flowing in a different direction than along the wire (perpendicular to the axis of the solenoid).

... "However soft iron although very difficult to magnetize permanently, is a ferromagnetic material with very small magnetic reluctance that would possible absorb all magnetic flux around the wire and confine it inside a hypothetical wire constructed by soft iron. Thus, a constant d.c. current carrying iron wire would be magnetized in contrast to a copper or aluminum wire which are not magnetic, creating possible its own magnetic moment m.

What would be the shape of the magnetic field on the soft iron wire?"

I think that the magnetic field due to the polarization of Fe magnetic moments will be zero because of symetry. As you say: "Therefore I expect in practice there will be no or negligible magnetic flux ..."

"... The iron will confine practically all the flux inside it having a magnetic shielding effect, isolating the magnetic field on in the wire from the surrounding air. We could say that iron wires are naturally magnetically shielded." Or non magnetically polarized (by a dc current) !!??

Carlos Ariel Samudio Pérez

As John Hodge suggested, whenever in doubt do the experiment. We should do the experiment. The easiest way I can think is just to wind a coil using soft iron rod as wire plenty available in the market. Shouldn't be very difficult. Then use a digital LCR bridge instrument to measure the inductance of the coil L and compare it with theoretical predicted value for an air solenoid (i.e. without an ferromagnetic core).

For example the predicted value for a normal copper wire air solenoid of 2cm radius 1cm length and 100 turns and μr(air)=μr(copper wire)~1 is calculated at L=1.58mH.

https://www.allaboutcircuits.com/tools/coil-inductance-calculator/

If the measured inductance value for the iron air coil comes out much different than the predicted then we know that the high permeability of the soft iron wire μr(iron wire)~ 5000 acts similar as if a ferromagnetic core was inserted inside the solenoid and disrupts the field inside the air gap of the solenoid changing therefore its predicted inductance.

I propose the first who does this experiment report back these results here in this thread. This would give us also data for a quantitative analysis of this possible effect.

Also, using a Hall magnetometer we can measure the magnetic field of the iron air solenoid at its center axis inside the solenoid. For example the predicted value for a normal copper wire air solenoid with the above dimensions 1cm length 100 turns at 1A d.c. current is 12.56 mT:

https://tinyurl.com/bsa8tadc

If the measured value differs much from the predicted then the iron wire must have changed the solenoid behavior.

I guess we all agree that the field of an iron coil is different from the field of a copper coil because, as you wrote yourself above, the iron acts simultaneously as a coil and as a core. So doing an experiment with a coil will not reveal anything new.

Why not start with a straight wire as in the original question, for example 1 m long, with additional wires forming a large closed loop? Using, for example, a cheap hall sensor Si7210 which can greatly reduce the noise by calculating the average of 4096 samples, plus a simple microcontroller board with alphanumerical display, one can well measure fields of about 30 μT, the geomagnetic field for example. In a distance of 10 mm from the axis of a straight wire carrying 5 A, applying the equation Malcolm White gave above, one expects H = 80 A/m and B = 100 μT.

By taking the difference of the results for both directions of DC current one can eliminate the effect of the geomagnetic field. Replacing the copper wire with an iron wire will reveal the truth.

Joerg Fricke

Great experiment! I agree.

"B=mo H =mo I/(2 pi r). This is the same for wire of any material."

Let's test the above statement.

https://sciencekitstore.com/soft-iron-rod-soft-magnetic-iron-rod-5-mm-x-200-mm-d-x-l/

Here is a soft iron rod 5mm diameter. I would prefer it without the nickel or aluminum coating but never mind.

The magnetic B field should be measured with a sensitive enough Hall or fluxgate magnetometer and compared it with a copper wire for the same amount of current passing through at 10mm distance from the naked wire surface.

No need for separate experiments. The two lead wires concreting the iron rod to the power supply will be from copper. Keep the wires aligned to the rod and straight and measure the B field on the iron and copper wire at the same radial distance 10mm.

It would be better to avoid any miscalculations in the distance if the copper wires have insulation, they should be made naked by stripping out their insulation. Alternatively, copper magnet wire could be used which has only a sub-millimeter insulation coating.

The soft iron rod on the above link seems to have a nickel or aluminium coating. If it is aluminium then there is no problem since it has practically the same relative permeability as air ~1. Nickel however has a relative permeability of 100 to 600. The nickel or aluminium could be scratched out in a small area of the rod to measure the thickness of the coating and then calibrate the distance measurement accordingly.

Because you will measure the same magnetic field in air at the same distance from the centre of the rod, for the same total current in the rod, coatings and layers (and materials) will make no difference, so do measurements with rods and wires as you find them, first, before using a lot of time and effort to remove coatings.

Malcolm White

You are completely right, of course, but if someone suspects that the theory of electromagnetism has overlooked the influence of conductor materials for 200 years then it's only natural to assume that so far the effect of coatings is misunderstood as well.

Otherwise, the question could be solved even easier by just reading the manual of a current clamp suitable for DC: If the sentence: "Be cautious! This instrument is adjusted for measurements of currents in non-ferromagnetic wires only." is missing, that's a strong clue. Additionally, one could just use a current clamp.

But I guess the presence of the iron core in the clamp makes things more complicated than necessary; that's why I suggested the use of an Si7210.

You are right Joerg Fricke. I suggested doing the simple easy measurements first, because if the theory is right they will be identical. Then remove coatings etc. if it is still necessary to find out more. But a measurement of identical fields with magnetic and non-magnetic wires, whatever the coatings, would be a fairly good indicator that all that matters for the field in air is the current through the loop.

https://sciencekitstore.com/soft-iron-rod-soft-magnetic-iron-rod-5-mm-x-200-mm-d-x-l/

The suggested soft iron rod above for the straight soft iron conductor experiment is according to the site, nickel plated which has similar electric conductivity with soft iron σ(nickel)=14x106 S/m. So there is no need for grinding the surface of the rod.

As for the soft iron air solenoid experiment I suggest this wire here:

https://www.etsy.com/listing/86030991/slimy-iron-wire-diameter-035-mm?ga_order=most_relevant&ga_search_type=all&ga_view_type=gallery&ga_search_query=soft+iron+wire&ref=sr_gallery-1-4

Malcolm White

Because the thickness of the different wires (i.e. copper or soft iron wire) used in the measurements may differ and to have a common reference, the 10mm distance measurement should be taken from the naked surface of the wire and not from the center of the wire. If the two types of wire are chosen to have the same naked thickness say 5 mm in diameter for example then yes the 10mm distance measurement can be taken from the center of each wire.

And to be more thorough lets take both measurements if the wires are of uneven naked thickness. One 10mm from the center of each wire and a second measurement 10mm distance from the naked surface of each wire.

The existing theory says that the field in air depends on the distance from the centre of the wire, not from the surface, so if the wires have different radii you will get different results for different wires if you measure from the surface of the wire.

Joerg Fricke

"the theory of electromagnetism has overlooked the influence of conductor materials for 200 years..."

Nobody suggests that the theory of EM maybe wrong. Ampere's circuital law says clearly that it is for an infinite long thus infinite thin conductor so that the permeability of the conductor medium μ can be neglected and only the permeability of vacuum space can be used μ0:

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html

The only reason why Ampere's circuital law today is also a very good approximation for any finite length and thickness conductor wires is because the materials used are normally copper or aluminum or silver which have relative magnetic permeability almost identical with that of air or the vacuum μr=1.

However, if the conductor wire material has a relative magnetic permeability much different than 1, like soft iron has ~5000 and has also a finite thickness, Ampere's law cannot be applied directly and is not a good approximation for a straight conductor wire in practice. The permeability of the conductor wire must be taken into account in this case and the B field varies inside the conductor with:

B= (μΙ/2πRW2) x r

where μ the absolute permeability of the conductor wire, RW the radius of the wire (i.e. thickness), I the current and r the distance from the center of the wire. From the above we see that the magnetic fiend Β in the wire reaches it maximum value at the surface of the wire r=RW. The above equation holds only for calculating the field inside the wire. After the surface boundary of the soft iron conductor is crossed for calculating how the magnetic field diminishes on air with distance the accurate equation becomes more complex. Again I repeat this all is only necessary when the wire material has a magnetic relative permeability much larger than 1 and a finite thickness.

Here is the analysis of Ampere's Law for a finite thickness wire conductor with μr~1:

https://www.youtube.com/watch?v=x4QRs-6PpOs

Also this analysis here that gives the same equation for inside the wire I have presented in my previous message,

B= (μ0Ι/2πRW2) x r (inside the wire for wire material with μr~1)

but not taking into account the case of the relative magnetic permeability of the wire being much larger than 1:

https://www.youtube.com/watch?v=EaHoufAMxL8

If this is the case the above expression should be rewritten as:

B= (μΙ/2πRW2) x r (inside the wire for wire material with μr>>1)

with maximum strength value of the magnetic field B reached for r=RW at the surface of the conductor Bmax= μΙ/2πRW

where μ the absolute magnetic permeability value of the wire conductor material. In case of soft iron it is μ=0.25 H/m.

Outside the wire for r>RW in the case of a soft iron wire conductor μr~5000 the magnetic field should then fall abruptly (i.e. non-linear magnetic shielding effect of iron) but cannot be calculated using the simple expression :

B= μ0Ι/2πr

where μ0 is the magnetic permeability of vacuum space.

These of course are my predictions that should be verified by experiments at 10mm distance from the naked surface of the two different type conductors (i.e. copper and soft iron) and the results compared.

Logic dictates that because the much less magnetic reluctance of the soft iron compared to the air medium the generated magnetic flux should be trapped inside the wire and no or very little flux should leak outside the wire (i.e. magnetic shielding) on air.

But of course I could be wrong.

Emmanouil

Emmanouil Markoulakis

You wrote: "Nobody suggests that the theory of EM maybe wrong."

But you do all the time, if not explicitely then implicitely:

"Ampere's circuital law says clearly that it is for an infinite long thus infinite thin conductor ..."

Ampere's circuital law (as published by Maxwell) says nothing about conductors at all. In integral form, it says that if you integrate the tangential component of H along a closed loop the result equals the current which flows through the loop. The current can be electrons in a bent wire, holes in a semiconductor, an evenly charged cylinder moving along its axis, or charged raindrops in a thunderstorm.

One nice aspect of units: They indicate what the numbers describe. In SI units, H has the unit A/m. Integrating along a line is equivalent to multiplying H by a length. So, the unit of the result is A * m/m = A. Just the unit of current!

"After the surface boundary of the soft iron conductor is crossed for calculating how the magnetic field diminishes on air with distance the accurate equation becomes more complex." It does, provided the cross-section of the ferromagnetic wire is, for example, star-shaped, and you want to know the field at a point near a spike. But if we are dealing with straight wires whose cross-sections are of perfect circular shape, and if we are integrating along a circle coaxial to the wire, then the field strength is the same at each point of the circle. Therefore, if we know the location of the axis of the wire, and the strength of the current (and nothing else) we can easily calculate H for every point outside the wire, and if we know the permeability of air, we can calculate B as well.

Of course, the most convincing way to find out is by experiment. I guess it would be of no use if I did it myself because I could provide only numbers, pictures, and perhaps a short video. I would not be surprised at all by the result, and you could not be sure whether I was pulling your leg (there are a lot of videos demonstrating perpetua mobilia, for example).

I don't know details about the semiconductor shortage abroad, but I have some Si7210s and some boards prepared for it on the shelf. If you cannot buy a suitable sensor at the moment, and if you tell me your postal address by pm, I would solder a sensor, a capacitor, and a connector to a board, and send it as a letter.

Of course, you would still need a microcontroller board; the interface of the sensor is I2C.

Prof. Emmanouil Markoulakis

I gave an answer related to your question in another thread, I used a slide, which is more comfortable for equations and proper citations, hope is related.

Best Regards, it is attached.

Dear Joerg Fricke ,

Thanks for your constructive arguments and suggestions for the experiments.

Again, whenever in doubt an experiment is the answer.

"Additionally, one could just use a current clamp."

This suggestion by you is actually the easiest and fastest for a qualitative conclusion. If I'm correct the Hall current clamp will falsely report the current in series whenever reading the iron rod segment in the circuit and correctly report the current whenever around a normal copper wire segment connecting the iron rod with the power supply. A current limiting resistor in series should be also used in the circuit.

The actual current could be further verified by connecting in series a digital Amperemeter.

Dear Prof. Pedro L. Contreras E. ,

Thank you for your expert input.

The debate here developed is, if the the strength of the magnetic field around a wire on air, created by the same amount of D.C. current will differ between a copper wire and a soft iron wire. In the highlighted equation you provided, it contains the magnetic susceptibility Χ of the the wire material. However, I don't know if this can me modified also to express the magnetic field around a given material wire on air?

May I ask you straight, what is your prediction? Will the magnetic field on air around a soft iron wire significantly differ in strength B from that of a normal copper or aluminium wire?

Yes, it will because Prof. E.Purcell won't make any mistake in his own calculation, I do believe the classist physicists' statements's.

Prof. Purcell's contribution in exp. magnetization of Iron is the highest one of any humankind I have read, Prof. Emmanouil Markoulakis

But in a couple of weeks, I could enhance my answer in another post if you allow me, please.

Best Regards & thanks for your fast reply.

This illustration summarizes the experiment.

I did an initial experiment:

https://www.youtube.com/watch?v=2Kmt42a3Ocs

The iron rod does not seem to react to current. No visible magnetic field around the iron conductor on air was detected. I will continue with more thorough experiments although the first qualitative test seems to confirm the far field shielding effect of an iron current carrying conductor wire opposite to a naked normal copper wire.

The rod I have used because it was accessory of drilling station I suspect is made up of carbon steel which has a relative permeability of 100:

https://www.engineeringtoolbox.com/permeability-d_1923.html

So not even close to the permeability of soft iron ~5000 therefore the shielding effect will be even larger in a soft iron rod. Of course the shielding of the magnetic field created by the current inside the wire will have no meaning if the iron conductor becomes a permanent magnet since the relative permeability of a permanent magnet is ~1 the same as air, copper or aluminium:

https://physics.stackexchange.com/a/301105/183646

Therefore soft iron is the best material since it is very hard to magnetize permanently and a very large current would be needed.

If you have your two wires in parallel, and are driving them with AC, then the high internal flux in the iron wire will give it a higher inductance than the copper wire so that more current goes through the copper wire. For the same drive voltage and negligible resistance the current in each wire is inversely proportional to its inductance.

You need a lot of current in a wire to get flux density noticeable bigger than the earth's magnetic field - for 1 amp in a wire the flux density in air 1 cm from the wire axis is less than the earth's magnetic field.

2 pi r H = current, and B = mo H. At 1 cm radius the flux density will be about 0.00002 Tesla (0.2 gauss) which is about 1/5 the earth's field.

You can think without fields as Ampère himself did. I suggest the book:

Book Ampère’s Electrodynamics – Analysis of the Meaning and Evolu...

or the articles:

Article Ampère's motor: Its history and the controversies surroundin...

Article Resuming Ampère's experimental investigation of the validity...

Article The Worldwide Simplest and Oldest Motor How does it operate?

Ampere's circuital law is correct.

The application of Ampere's circuital law on cylindrical conductors states also wisely, which is by many ignored or misunderstood that the wire must be infinite long which also therefore means infinite thin having no thickness and therefore the permeability of the wire can be ignored if different from the air or vacuum μr~1.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html

In practice this also the case for a normal wire conductor (e.g. copper) of finite thickness surrounded by air or vacuum since they all have the same relative permeability ~1.

However, in the special case of an iron wire conductor surrounded by air we have two distinct separate medium with much different magnetic permeability values and a finite thickness iron conductor which cannot be ignored by the general application of Ampere's law for cylindrical conductors.

What I mean is Ampère has never thought in terms of fields. And that Ampere's circuital law is not from Ampère's theory. The founder of electrodynamics has proposed a different theory and pointed out very incongruousness in how the EM is today modeled (He criticized Faraday's view and, in essence, the current view's foundations). It is just something to think about, another way to look at the problem if you like...

Malcolm White

After the initial experiment demonstration linked video. I repeated the experiment for 5A (B=1G at 1cm) and went up to 8A with the same result. No motion of the compass needle on the iron rod whereas the copper wire connected electrically in series with the iron rod therefore the same current flowing I, demonstrated a strong motion of the compass needle. The predicted field value at 1cm for 8A is 1.6 Gauss almost x4 the average magnetic field of the Earth which varies between 0.25G to 0.65G.

https://en.wikipedia.org/wiki/Earth%27s_magnetic_field

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html (calcualator)

In my location the Earth's magnetic field is ~0.4G.

The copper wire segment and iron rod measured were aligned in the same direction but not parallel to each other. The attached illustration summarizes the findings of this experiment.

I suggest his experiment has a problem. The iron is magnet attracting. Therefore, the needle points to the rod. The generated current is 1) insufficient to change this attraction and/ or 2) the possible B field is around the wire. Note the copper wire case the needle moved SLIGHTLY to reflect a perpendicular orientation to the wire. But the magnetic wire strength was too weak to completely overwhelm the Earth's field. So, initially (0 current) the pole of the compass pointed to the wire - the end point - therefore, not test.

The ideal position is the magnet (compass) should be under the wire. Bt the wire field would be too weak to affect a magnet (say N pole) the distance of 1/2 the length of the compass needle - say centimeters. This test is too insensitive.

The advantage of the following experiment structures is that the distance between magnet and wire is small (approximately 0.05 cm).

https://www.researchgate.net/publication/329371487_Magnetostatics_relation_to_gravity_with_experiment_that_rejects_Biot-Savart_Law

https://www.researchgate.net/publication/327157853_Another_experiment_rejects_Ampere%27s_Law_and_supports_the_STOE_model

Another implication is that the integration along the length of the wire is incorrect. I note that in the experiments that determine \mu, the 2 wires are parallel for a considerable distance. So, the above experiment suggest only the perpendicular distance matters is satisfied for both wires being long. This is why a disc magnet of only a short width was used.

The following experiment also indicates limited field of induction.

https://www.researchgate.net/publication/327158807_Two_different_types_of_magnetic_field

The above (Biot-Savart) experiment is easy to re-do. Especially if you have 5 - 8 amp. supply available. I'd be interested if you re-did it.

Dear John Hodge ,

Yes I mentioned also this observation inside the video.

In order to exclude any static magnetic dipole interaction of the compass permanent magnet with the iron rod I will therefore repeat the experiment with a Hall effect current clamp to be sure. A colleague of mine promised me he will bring me the clamp soon.

(under normal operation of the iron conductor circuit there is no magnetic dipole interaction assuming there is no an external permanent magnet near the circuit therefore the only magnetic field present should be that generated by the current I flowing through the iron conductor which is not a normal dipole magnetic field but a closed loop magnetization field).

The compass itself is a very small permanent magnet but very weak. By approaching it to a ferromagnetic material it will generate a dipole magnetic field on the ferromagnetic of opposite polarity thus attraction. I noticed however that the compass needle at the distance and relative position I've placed it, is not totally pointing towards the the iron rod when the power is switched off but holds an angle which means that the small ferromagnetic attraction of the iron rod by the compass needle permanent magnet is comparable in strength to the magnetic field of the Earth.

Therefore almost doubling the current I, from 4.2 A to 8A should produce a visible motion in the compass needle which however did not and the compass needle remained still in the same position.

Placing the compass above the copper conductor wire or iron rod symmetrical at the center is not a fair comparison because the copper wire in the experiment is much smaller size (i.e. thickness) than the iron rod and the compass disc is relative large in size (i.e no point probing of the field). If I had a smaller size compass comparable with the size of the conductors then yes but not with the current compass. Opposite to the generated by current magnetic field in the iron rod the ferromagnetic induced magnetic field by the permanent compass dipole magnet on the iron rod is not confined inside the iron rod but spread depending also the physical length of the rod, outside the rod on air.

Repeating the experiment without any external magnet being close to the ferromagnetic rod will give us conclusive results.

Emmanouil

Emmanouil Markoulakis

Perhaps. Thanks for your effort.

Placing the compass under the wire should be done so the circular N-S field of the wire covers both poles of the compass. Usually this is done by placing the compass some distance from the wire. A smaller compass or a thin magnet such as the disk magnet used in the Biot-Savert experiment suffices.

John Hodge ,

I don't have yet the Hall current clamp so I thought I repeat the experiment this weekend with the compass positioned this time above the conductor at the center of the compass as you have suggested.

Please read the description in the video:

https://www.youtube.com/watch?v=6fNniRL2cQM

Thanks. I like your videos.

Suggest turn the iron 90 degrees to the earth's mag field. The N-S axis of the compass should be 90 degrees to the current flow. as seen with the copper wire.

Does the wiggeling of the needle above the iron suggest some current effect in the iron rod?

John Hodge ,

I used the degree scale on the compass to measure accurately the steady state displacement angles of the compass needle between the vectors of the current and the Earth's magnetic field:

I(copper) ⊥ B(Earth)= 120° (Clockwise displacement of compass)

I(steel) ⊥ B(Earth)= 10° (CW displacement of compass)

I(copper) || B(Earth)= 80° (CW displacement of compass)

I(steel) || B(Earth)= 5° (CW displacement of compass)

For I=I(copper)=I(steel) = 4A, B(Earth)~40μΤ (0.4G) in my lab location and Ampere's law general application for infinite thin conductor current generated magnetic field at 1cm distance on air B(Ι)= 80μΤ (0.8G).

μr(air)=μr(copper)~1

μr(steel)~100 (estimated).

You can construct an "astatic" needle i.e. a needle that "ignores" Earth's magnetism. There are two models that Ampère made.

I strongly suggest the reading :

Book Ampère’s Electrodynamics – Analysis of the Meaning and Evolu...

The one of the astatic needle models are in p. 60 of this book and the other is in figure 15 of AMPÈRE, André-Marie. Suite de la Note sur un Appareil à l'aide duquel on peut vérifier toutes les propriétés des conducteurs de l'électricité voltaïque, découvertes par M. Ampère. Annales de chimie et de physique, 1821, t. 18, p. 313-333

Emmanouil Markoulakis

Interesting.

I notice the needle jumps when the current ti turned on and off. That is the "jump" is deviate from the established position. Then return to the iron to magnet position with both current on and off. The Copper did not do this - the needle changed to the perpendicular /current on position.

Suggest turning the iron rod 45 degrees and repeat. do we get the same neutral positions?

This suggest to me that whereas the current in Cu wire id carried on the outside of the wire, the current of the Fe wire is carried in the body (?) I don't understand this mechanism.

Interesting.

John Hodge

"I notice the needle jumps when the current ti turned on and off. That is the "jump" is deviate from the established position. Then return to the iron to magnet position with both current on and off. The Copper did not do this - the needle changed to the perpendicular /current on position."

That is because a large portion of the Earth's magnetic flux on air is channeled axially along the length of the copper wire with the current switched off. You could say that the Earth's magnetic field is diverted locally to the axial orientation of the iron rod every time, inside the iron rod. However, on air the remaining flux of the Earth's magnetic field remains I believe unchanged around the iron rod and also when the current is switched on the Earth's flux channeled inside the rod is expelled from inside and replaced by the current generated magnetic concentric rings flux inside the rod. The concentric ring current generated magnetic flux interacts with the normal Earth's magnetic field flux on air.

Just wait for the current clamp. I will have it by this Monday. This will give us a conclusive result of the magnetic field strength around the iron rod when the current is switched on. If I'm correct then the clamp will report falsely the current value in the circuit whenever positioned around the iron rod. We can find the correct current value with the Amp meter connected in series which should match the clamp reading whenever this is around the normal copper wire conductor.

Interesting. I note Maxwell's equation addition relates the changing ELECTRIC field to the magnetic field around the wire. Perhaps the Cu wire saw this but the end result is where the needle jumps to.

The next is to investigate the effect of a bit more distance between the wire and compass. The compass needle acts by torque. the longer the arm, the easier the attraction of the iron is to influence the needle. So, the effect on a smaller compass, or on the compass further from the iron [The mag field from the iron current is inverse squared (?). the effect of the poles on the compass is inverse distance CUBED (?) - I'm a bit unsure of this].

You and Andre influenced my efforts on magnetics a few years ago. I tempted the get the equipment and play. But you have a good current generator.

John Hodge ,

According to Ampere's circuital law application for cylindrical conductors, since the field of concentric rings is not open bar dipole magnet field but consisting from closed magnetic loops it does not fall with the inverse cube with distance but linearly as 1/r. This is of course for an infinite long wire so I'm not so sure if this applies in practice?

The force (gradient of field strength?) of a dipole such as in the compass and as in an electric dipole fall as inverse cube to the side of the diploe (?) (where both poles have an inverse distance squared effect - my memory may not bee too good here, but it seems this is shown in texts). So the torque falls faster than the force of the current induced magnetic field. Seeks like something to measure.

How could your equipment be fitted with a force measuring device? I'm becoming integer. Perhaps I should make a setup of my own. It would have to be cheap. Perhaps use batteries DIRECTLY connected for basically short circuit operation. But such a system would be uncelebrated. Ah, well!

Final experiment with conclusive results:

Negative Results Magnetic field on air around a current carrying ferromagneti...

I was wrong in my hypothesis however glad that I performed this experiment since there is no other reference on the internet or literature as far as I know about the magnetic field around a ferromagnetic current carrying conductor (D.C. current) and happy about the result and conclusion reached.

It was proven from this three part experiment (see also my previous two experiment videos with the compass1) that although the magnetic field created by the current inside the iron ferromagnetic conductor is much more stronger than a normal copper conductor due to the much higher relative magnetic permeability of the iron, on air the magnetic field created around the conductor is independent the material of the conductor (i.e. ferromagnetic or non) and depends only on the current I passing through the conductor. It seems that the same amount of magnetic flux in Weber SI units is created on air around the conductor cylindrical wire independent the material and depending only from the current value inside the wire.

Therefore, although soft iron can be used as mantle on conductor wires for magnetostatic shielding or low frequency magnetic fields it does not offer any magnetic shielding effect when used as the current carrying conductor in the wire the same as normal copper or other electric conductor materials which are not ferromagnetic. The strength of the magnetic field on air (or vacuum) around the wire will be always the same for a given distance from the center of the wire and a given current flowing inside the wire independent of the material of the wire.

Analytically using Ampere's circuital law application for infinite thin conductors the magnetic field on air around the conductor will be:

B= μrμ0Ι/2πr (1)

(for μr~1 relative permeability of air and r the radial distance from the center of the conductor). Notice, equation (1) above cannot be used to calculate the magnetic field inside the conductor r

Dear Malcolm White and Joerg Fricke ,

I was wrong in my hypothesis you are correct.

However, this had to put into test and I'm happy with the negative results of my experiment that proves Ampere's circuital law application for the magnetic field on air around the conductor holds also for ferromagnetic conductors.

Best Regards,

Emmanouil

Thank you Emmanouil Markoulakis . I am pleased that you have managed to do the experiment accurately enough to prove this to your satisfaction.

The result and final conclusion of the experiment is actually IMO non intuitive.

An outer iron mantle on a cable similar to an iron pipe encompassing the conductor current carrying copper wire inside, separated by an insulator layer form the iron shield mantle, will actually shield magnetostatically any magnetic flux generated by the copper conductor wire leaking on air outside the cable and also from an external magnetic field trying to enter the cable towards the inner wire conductor which we know is not the case if a copper shield was used instead since this material cannot offer any magnetostatic shielding as iron does,

however, surprisingly when this same magnetic shielding material is used the iron, as a conductor current carrying medium it does not offer any magnetic shielding effect and the magnetic flux leaks normally outside the conductor on air as predicted by Ampere's circuital law?

This is a fascinating and may I say intuitively unexpected result and phenomenon.

What is the physical explanation for this apparent contradicting behavior?

My explanation is that the Law of Physics that relates electric current(I) and magnetic flux (φ) is Ampere’s Circuit Law.

(see attached figure)

It states that the line integral of magnetic flux density(B) along a closed path is equal to the current (I) enclosed by the path multiplied by the absolute permeability of the medium μ=μrμ0. The medium in our case is air which has the same absolute permeability with vacuum space μ0.

So the total amount of magnetic flux Φ in an Amperian loop of surface area A generated by an electric current I inside this loop will be always the same value for the same current value Ι and distributed in a density (i.e. B= Φ Α field strength) according to the radial area of the Amperian loop each time and the current value I as long this medium inside the Amperian loop is uniform.

The important thing to notice here is that the total amount of magnetic flux generated in an Amperian loop of area A and current I inside is also a property of the absolute permeability of vacuum space μ0. So the total amount of magnetic flux generated depends form the the current I, the loop surface area Α and the product of μ=μrμ0 thus the absolute permeability of the medium.

The above characteristic and equation tells us that the amount of magnetic flux generated inside a medium different than the vacuum by a current, is the amount of magnetic flux if the medium was the vacuum μ0 multiplied by a factor μr. This may come as a surprise for many but don't forget that in matter most of the space between the atoms is vacuum.

Therefore in our case of the experiment where the Amperian loop encloses two vastly different permeability medium, iron μr=5000 and air around the iron conductor (i.e. air is practically same as vacuum case) there is indeed much more total magnetic flux generated than in the case of a copper conductor μr~1 surrounded by air. However, the amount of magnetic flux on air around the two different conductors remains the same independent the conductor material inside our Amerindian loop. The extra amount of magnetic flux generated by the iron conductor is isolated inside the conductor and does not subtract any amount of the flux on air.

This was my initial mistake in my thinking. I though the total amount of generated flux depends only by μ0I and then the flux is distributed accordingly to the relative permeability value of each medium separately. Therefore I thought the iron would take in most of the flux leaving less on air. It never crossed my mind that the iron conductor case generates more total flux than the copper conductor case, inside an Amperian loop enclosing both, conductor and surrounding air but this extra flux remains isolated inside the iron and does not affect the flux amount on air.

Actually for the boundary condition r=Rw we find for μr(iron)~5000 times more magnetic flux inside the iron than in the case of a copper wire of the same radius Rw.

Emmanouil Markoulakis ,

the explanation: You did a first step into the right direction by doing the experiment using a current clamp. Your next fine step was to accept the result! But that's not enough because otherwise you'll end up with a set of partly wrong concepts and another set of experimental results connected to your concepts only by their being apparently paradoxical.

The missing step is to adapt your concepts to the experimental result.

You wrote: "An outer iron mantle on a cable similar to an iron pipe encompassing the conductor current carrying copper wire inside, separated by an insulator layer form the iron shield mantle, will actually shield magnetostatically any magnetic flux generated by the copper conductor wire ..."

and: "... when this same magnetic shielding material is used the iron, as a conductor current carrying medium it does not offer any magnetic shielding effect ..."

and then you observed quite correctly that these statements can hardly both be true.

So, since the second one is proven experimentally, obviously the first statement is wrong.

As I wrote before, if you know exactly what is going on you can use the term "shield" as an abbreviation, engineering-wise; otherwise you have to explain (at least to yourself) how the "shielding" is effected by superposition of secondary fields. You will not succeed in explaining the first statement by superposition. Consequently, your concept of "shielding" has to be replaced by a more useful and true concept.

Emmanouil Markoulakis

If there are several wires in a bundle, with the outgoing and return currents included, so there is no net current, then outside the bundle there will still be some residual flux because the wires aren't all in the same position and their fluxes don't quite cancel. In this situation the magnetic shield around them works to reduce the leakage flux outside the shield. If there is any one-way current in the bundle, the shield won't reduce it the flux due to that current, even if none of that current flows in the shield.

Obviously as the experiment shows there is clear difference in behavior of ferromagnetic materials as a current carrying conductor generating its own field and as a passive shielding material for magneto static or low frequency (up to a few KHz) magnetic fields.

Especially, for magnetostatic fields (zero Hz) soft iron or mu-metal have been proven an effective shielding mechanism redirecting due to their low magnetic reluctance most of the magnetic flux inside the ferromagnetic shielding material and are used for shielding hundreds of years now in pair with Faraday cage shielding of EM waves using a mantle of copper or aluminium mesh around the conductor wire (coaxial wire).

Of course no shield is perfect and a small amount of flux will leak outside the shield.

"If there is any one-way current in the bundle, the shield won't reduce it the flux due to that current, even if none of that current flows in the shield."

Ferromagnetic magnetostatic shields opposite to EM Faraday cage copper wire shields are not grounded and will "absorb" most of the static magnetic flux. Also because the static magnetic field generated by the shielded conductor copper inside the cable due to D.C. current, there are no induced currents in these shields so that the ferromagnetic shield does not become current carrying which would generate a magnetic field on air. Therefore the magnetostatic shielding of a single conductor cable (i.e. one-way current carrying wire) will work just fine IMO.

Mu-metal because its very large permeability (much larger than soft iron) is the ideal static magnetic shield but for low strength B fields because its low saturation magnetization value. Therefore, for strong magnetic fields a type of soft iron is the better static magnetic field shield choice which has a much higher saturation value. Sometimes, combination of both mu-metal and iron is used.

https://en.wikipedia.org/wiki/Mu-metal (image source)

Heaviside found theoretically that the prerequisite for undistorted signal transmission is G/C = R/L, and that the cables used so far had an L that was too low. The purpose of the Mu-metal in the picture above is to increase the inductance (without any effect in the DC case, of course).

https://en.wikipedia.org/wiki/Heaviside_condition

I feel it's time for another experiment, so I suggest that you get hold of an iron tube (Mu-metal is expensive), and ask your colleague once more for his/her current clamp.

Dear Joerg Fricke ,

A detailed description of the illustration attached in my previous message of the WP article describing mu-metal https://en.wikipedia.org/wiki/Mu-metal can be found here:

https://en.wikipedia.org/wiki/File:Mu_metal_submarine_telegraph_cable_construction.svg

In this picture the naked mu-metal wire is used as a winding around and in physical and electrical contact with the copper core conductor (i.e. no insulation layer) adding inductance to the transmission line thus, increasing the inductance of the copper core conductor by increasing the magnetic flux on the core conductor, in order to balance out the parasitic capacitive coupling of the sub-marine cable with the seawater which was acting as a secondary conductor degrading the transmitted signal quality especially at higher signal frequencies.

The choice of mu-metal in this case for the inductive loading winding of the core conductor was justified because the very high relative magnetic permeability of mu-metal thus a ferromagnetic material, is increasing significantly the inductance of the core copper conductor in the transmission line acting effectively as a ferromagnetic core.

This information was also inside the linked WP article explaining the history of mu-metal applications:

https://en.wikipedia.org/wiki/Mu-metal#History

Since this was a 1923 telegraph cable therefore low frequency signaling (i.e. few KHz), ferromagnetic "absorbing" RF shielding was the obvious choice instead of reflecting Faraday cage RF electric shielding since at these low frequencies this type of shielding is not so effective.

A.C. or pulse-transient current or RF in general in single conductor wire is different from the D.C. case in my previous experiment, since now inductance L is part of the equation . Effectively, the mu-metal even in electrical contact to the copper core conductor, did actually shield the signal from the seawater by increasing the induction of the core copper wire and therefore confining the magnetic flux in the wire and not allowing the signal voltage along the transmission line to degrade significantly due to parasitic capacitive coupling with the seawater.

So, yes in the case of RF signal carrying wire the magnetic field on the seawater surrounding the wire is less with the mu-metal inductive loading added to the core copper conductor. So indeed the mu-metal acts effectively as a ferromagnetic RF shield in this case by changing the electrical properties of the core conductor copper material and even if the mu-metal winding becomes current carrying itself.

The iron armor shown in the illustration is further additionally shielding magnetically the RF signal carrying wire.

"I feel it's time for another experiment, so I suggest that you get hold of an iron tube (Mu-metal is expensive), and ask your colleague once more for his/her current clamp."

I'll see what I can do for you. Let's find an iron pipe :)

Emmanouil

image source: https://atlantic-cable.com/Article/EnderbyAG/index.htm

Here is an interesting article about passive magnetic shielding by K&J Magnetics:

https://www.kjmagnetics.com/blog.asp?p=mumetal

I found a ferromagnetic pipe about 14 cm long and 3 cm diameter and 1.2 mm thick. But since the d.c. current clamp has 1A digital display resolution with +/- 0.3A analog uncertainty I could not accurately decide the amount of field reduction by the passive magnetic shielding of the iron tube.

However, I have set a 0.85A d.c. current on the power supply and the current clamp when over the copper wire without the iron tube passive shielding, its display was fluctuating between 0A and 1A reading whereas when over the copper wire with the iron tube shielding the display showed constantly 0A.

So the iron tube 1.2mm thick must have "absorbed" some amount of magnetic flux generated on air by the current in the copper wire. Again only a qualitative result not a quantitative so it should be taken with a grain of salt.

Dear colleague,

The magnetic field is like a viscous fluid.

Arbab