Similarly, a changing current solenoid will generate the same fields as shown in the illustration for a charging/discharging capacitor, only now the circular blue field is the induced electric field E (or else called magnetic vector potential) and the straight red field is the changing magnetic field B inside the solenoid.

Fair use image credits: Addison Wesley Longman, Inc. (image was taken from this link here, https://physics.stackexchange.com/questions/421158/magnetic-field-from-displacement-currents-in-a-capacitor-and-an-applied-exterio ).

Dear Emmanouil Markoulakis ,

You can't magnetize iron within a variable capacitance since you will have an oscillating magnetic field giving the resulting magnetization zero. The induced magnetic field will be positive.

In the case of a variable magnetic field, you'll induce a negative electric field (induction), also here no magnetization.

JES

I fully agree with Dr Stellan Gustafsson,

"You cannot magnetize iron within a variable capacitance, as it will have an oscillating magnetic field that will give zero to the resulting magnetization, ..."

Iron (bcc-Fe) is already a magnetic material, just with its randomly oriented magnetic domains. Therefore, the magnetization field must have a preferred direction for magnetic ordering to occur in the sample.

What if the voltage across the capacitor is DC (not changing)? Still an electric field, but no current flow. I think it's worthy of an experiment because of its implication to Maxwell's equations.

If what you want is a didactic discussion, I think it would be more interesting to analyze, from an experimental point of view, whether it is possible to self-induce the magnetization of an iron bar using a flux of "thermal current".

What about the area around the air gap of the capacitor?

Iron filings are discrete ferromagnetic pieces resembling needles and have therefore a very low magnetic reluctance, https://en.wikipedia.org/wiki/Magnetic_reluctance that would in practice dump down any minor oscillations you have mentioned. The ring structured magnetic field due to the displacement current may vary in density of flux during charge or discharge of the capacitor but the geometry of the field (i.e. concentric tings) would remain the same.

I don't see any reason, given enough power, the iron filings not to align to concentric rings and remain in that position around the capacitor and inside its air gap after the capacitor is fully charged or discharged. It may take several cycles because the mass inertia of the iron filings but I believe at the end you may be successful in getting the imprint of the magnetic field of the displacement current.

Maybe I was not understood correctly? In my proposed experiment you don't feed the capacitor with a continuous a.c. signal rather you charge with a manual switch from 0V to +V and then discharge it from +V to 0V. You repeat this cycles several times until you get the imprint of the field with the iron filings.

Nevertheless, to be sure only an experiment can tell and since as far as I know this was never demonstrated before in the literature I believe it is worth the try.

I think the initial question is that it was not clear:

Can you magnetize the wire by placing it in the air gap of a two-plate capacitor?

You didn't speak of aligning iron filings, but of permanently magnetizing the iron!

Good look

Dear Carlos,

Sorry for not making clear myself.

Kind Regards,

Emmanouil

I agree with the answer at physics.stackexchange as regards the Hc field caused by the conduction currents. If not taken into account the result of any experiment seems to be worthless.

I did a quick and dirty calculation for the case: radius of plates 50 mm, distance of plates 2 mm, point under observation midways, i.e. 1 mm from each plate. Assumptions: current on the wire everywhere the same (wavelength much longer than dimensions of capacitor; doubtful), even charge distribution on plates (doubtful, too), current enters the plates at the center on the inside (e.g. through some holes near the center).

Obviously, between the plates, the Hc field caused by the wires and the Hc field caused by the radial current on the plates point in opposite directions. The attached file shows the dependence of the sum of both Hc components on the distance to the center.

Since there are zeros at about 3.5 mm and 36.5 mm distance from the center, the iron particle(s) should be placed at about 36.5 mm in this case. Here only the field Hd, accompanying the displacement current, can influence the iron.

Emmanouil Markoulakis

Yes, that would also be interesting. I was thinking more of a DC potential -not bring iron into possible field until after the DC is established. Lightly tapping the support of the filings could do the same as shocking.

The switching on and off is still a varying electric field.

Research Proposal Two novel fundamental electromagnetic proposed tabletop experiments

You could magnetise iron, but not in the centre of the air gap. The integral of the magnetic field around a loop (H.dL) round the wire leading to the capacitor, or around the capacitor, is equal to the electric current or displacement current through the loop. The loops between the capacitor plates may be roughly circular, depending on the shape of the capacitor, and the displacement current through a loop is proportional to the area of the loop, and the magnetic field also inversely proportional to the perimeter of the loop, so the magnetic field increases linearly with distance from the centre. This only happens when the current is flowing, i.e. when the capacitor is charging or discharging.

You need large currents in a wire, or lots of wires with a bit of current. That is why a solenoid has lots of turns, or very thick conductors. Our magnet charger used a single secondary turn of a transformer, with 2.5 cm diameter copper rod with a massive current in it.

You could also magnetise iron by rapidly moving it from the edge to the middle of the capacitor, when the capacitor was charged. At the very least there would be induced conduction currents in the iron that would magnetise some of it. There would also be some current into the capacitor (if it was constant voltage), because the capacitance is higher with the iron in the gap than without.

Malcolm White

Thank you very interesting suggestions and explanations.

It would be nice one who has experience and the means to actually try to obtain an imprint with iron filings of the magnetic field due to the displacement current in a capacitor. This as far as I know would be a novel experiment worth a publication and also a demonstration video in youtube or other media.

Kind Regards,

Emmanouil

p.s. Also there is an open question if there will be an imprint of the magnetic field with iron filings inside the air gap area of the two parallel capacitor plates?

The answer may not be so straight forward especially if the iron filings are rusted (iron oxide dielectric) since then the iron fillings can be also electrostatically charged. In that case the final trajectory of the iron filings may be a subject of the EM Lorentz force vectors. The experiment should be repeated with rusted iron filings and clean of rust iron filings (use appropriate solution to remove any oxidation layer) and possible different results should be compared.

Also the plates of the capacitor each should be thick (e.g. 3cm) to be sure that the pattern of the magnetic field is not caused by the terminating wires at each capacitor plate but actually by the plates themselves.

I am not sure if your question refers to permanent magnetization or temporary magnetization.

If soft iron was used then after all currents have stopped and nothing is moving the iron will not be magnetised, although it may still be in the shape of the fields that temporarily existed while there was current/movement.

Iron used to make patterns for display usually does not remain magnetised much when the external field is removed - in other words it has a low remanence, otherwise the filings would all clump together when there was no field. This is called a soft magnetic material. Whether materials remain magnetised when the field magnetising them goes away depends on the initial material and the mechanical processes it has undergone, and the resulting crystal structure, for instance. Materials with low remanence are used in applications where they will be magnetised and demagnetized often, for instance, because work is needed to overcome remanence and this makes the material hot each time the magnetic field is cycled, which is a bad idea in a transformer yoke, for instance. Materials with higher remanence are used where permanent magnetic properties are needed.

One of the reasons permanent magnets that need aligning need such high currents/magnetic fields to magnetise them is that the remanence has to be overcome, for the magnetisation of all the parts of the magnet to be dragged round to roughly the right direction. It is a bit like the force that would be needed to cold-forge a spanner, which is much greater than the force that the spanner is to be used for.

Dear Malcolm White ,

Thanks for your valuable expert input and clarifications provided.

No, by "magnetize an iron" I refer more to its very low magnetic reluctance characteristic that makes a needle shaped iron piece to align each to the vectors of an external magnetic field.

So no, I am not referring to permanently magnetize it which you are right soft iron is very difficult to magnetize permanently although soft iron type of iron filings (not magnetite) will remain for a little while magnetized (small residual magnetism) after the external field is withdrawn. I hope this is the case also for the capacitor experiment I am proposing thus after the capacitor is fully charged, the iron fillings will remain in their magnetized orientation in order to observe the field pattern imprint.

Kind Regards,

Emmanouil

Paper was updated, see green text and calculation of the second experiment's capacitor characteristics and power supply was added.

Research Proposal Two novel fundamental electromagnetic proposed tabletop experiments

Emmanouil Markoulakis

Assuming iron is electrically insulated from capacitor plates, applying AC on the capacitor plates is a well known way to demagnetize iron, which was often used in laboratories where I worked.

Essentially no external magnetism occurs except maybe briefly a small amount as the iron is being inserted.. The E field crosses between the capacitor plates. So the H field must circle around the iron plate and essentially parallel to the capacitor plates for any orientation of the iron plate. AC reverses the H field direction clockwise or counter clockwise and dissipates by hysteresis any circular magnetism that might have preexisted in the iron plate cross section that is parallel to the capacitor plates.

During operation of the capacitor plates with DC no power comes out because the H lines of force are closed circles. AC power makes H lines as open spirals, continually changing directions and a Poynting vector comes out as an EM field radially from the centerline of the air gap.

DC power on the plates can make a closed internal magnetic domain inside the iron plate, but none of the resulting magnetic field comes out of the iron plate unless it is cut, notched, or broken by non destructive means.

Notice that we make magnetic motors not electrostatic motors, because the E force is much less than the B force for the same power applied. That said a weak permanent magnet may be made of hard iron using strong DC power on the capacitor plates, if a segment of the iron is notched out later after removal from the capacitor, exposing magnetic poles to the air of the other wise hidden internal magnetic domain.

B/μ = (H + M)

E = Bc for light speed c

c = 1/(μϵ)(1/2)

Z = (μ/ϵ)(1/2) or about 377 ohms in vacuum space

E = Z(H + M)

A large electric field is required to accomplish the same work as a small magnetic field.

Jerry Decker

Thank you for your expert description and analysis.

I agree with your analysis that because the closed ring magnetization similar to a torus solenoid there is no magnetic field B=0 outside the iron filings rings formed. This will of course not impend the concentric rings magnetic field imprint formed by the iron filings around the the capacitor. Also I assume there is no fringing E field generated or negligible around the capacitor because the close distance (2mm) of the two capacitor plates.

The problem is more complicated and concerns my question here, what will be the net field imprint shape in the air gap of the capacitor. The resulting imprint depends greatly from the type of sensor we are using and its ability to sense either the E field or the H field or maybe both, in the air gap of the capacitor between the two plates? The proposed sensors here the iron filings. Iron is a material as we know that can momentarily (before it reaches electrostatic equilibrium) electrostatically charged and also for more prolonged period if it is also rusted (iron oxide dielectric) but also opposite to other metals like copper, can be also magnetized (ferromagnetic material).

Because the iron filings will be also in one degree oxidized (dielectric on the surface) there can be also a good chance that they will also be electrostatically charged during the power on charge transient of the capacitor. Therefore, the iron filings would sense and respond to both E and H field generated during charging of the capacitor (we are not considering discharge).

My question therefore is assuming the capacitor plates are isolated and no shortcircuit can be caused by the iron fillings in our D.C. circuit and assuming that the iron filings will keep due to their inertia their polarized orientation and imprint of the EM field after the capacitor is fully charged, what will be the shape of the corresponding imprint we will see of the iron filing placed inside the air gap of the capacitor?

See possible answers a, b, c or d in link below:

https://physics.stackexchange.com/questions/710327/em-lorentz-force-field-flux-in-the-air-gap-of-a-parallel-plates-charging-capacit

I asked this in PSE and got no answer!

The problem is that during charge of the capacitor there are no discrete electric field E and discrete magnetic field B in the air cap of the capacitor as wrongly for pedagogical reasons and simplification illustrated on the attached figure.

Two different vector force fields cannot occupy the same space and be discrete from each other at the same time since that would mean that for each point in space we would assign two different vectors which may be mathematically acceptable as an analysis method but is physically impossible. Instead that what is happening is actually physically, there is only one net EM force field and net flux generated in the case of the iron filings during capacitor charging inside the air gap, described by the Lorentz EM force field F=q(E+B x v) equation and also magnetic torque equation τ=mxB.

(Note: Don't be confused by the field imprint obtained by different types of field sensors. Using castor oil and semolina seeds would for example sense only the electric flux component of the the EM field since these cannot be magnetized. However, there are no two different separate electric and magnetic flux fields physically present with the flux of each intersecting the flux of the other. There is only one unified EM flux vector field present described by the full Lorentz force equation physically present, inside the air gap of the capacitor during charging. Of course after the capacitor is fully charged and remains charged in our D.C. circuit there is only the E flux axial field left running accros the two capacitor plates)

Therefore IMHO the resulting imprint by the iron filings is answer c (spiral imprint) from the above provided url link assuming that the iron filings during capacitor charging can be simultaneously be electrostatically charged and magnetized. The iron filings field sensors would in that case inside the air gap of the capacitor during charging respond to the full EM Lorentz force and not just the Electric and magnetic component and therefore the resulting imprint would be spiral.

Jerry Decker

There is now a separate question thread created concerning the specific field imprint in the air gap of a charging capacitor using iron filings because it seems this subject grants further investigation:

https://www.researchgate.net/post/EM_Lorentz_force_field_flux_in_the_air_gap_of_a_parallel_plates_charging_capacitor

If the iron plate is assembled from segments before or after placing it in the capacitor, then a strong DC charge would create a hidden magnetic domain that would be discovered by separating the segments after removal of the iron from the capacitor.

The shape of imprint for a DC charge will be closed circles, except a spiral shape may occur briefly while the capacitor is charging.

Dear Jerry Decker ,

I fully agree with you theoretically in your last comments. Assuming these hypothetical iron plate segments (usually capacitor plates are made up of non magnetizing material like copper or aluminum and not iron) you describe do not hold any residual electrostatic charge but only residual magnetism and leak current is negligible after the capacitor is fully charged there is no displacement current nor electron current in the circuit after the capacitor is fully charged therefore no more magnetic field is generated and only the axial electric field E is present across the two plates of the capacitor. The final residual magnetic imprint will therefore essentially revert from momentary being spiral during charging due to the full Lorentz force influence, to concentric circles.

This is logical since the displacement current in the capacitor during charging is equal with the electron current in our D.C. circuit which after its initial exponential zero to 4t RC time period abrupt change then stabilizes at the last charging period 4t o 5t to constant value similar to a D.C. current carrying wire. Therefore the final residual imprint on the magnetic plates segments cannot be different than the shape of the magnetic field on the connected wires to the plates thus concentric rings.

In practice however my only concern is that during the final stage 4t το 5t the charging current although nearly constant is very small in amplitude and would be thus also the magnetic field it creates and be not enough to leave an imprint of the field created by the iron segments in contrast to the much larger current during initial charge of the capacitor 0 to 4t time period therefore also a much stronger magnetic field and the spiral imprint it creates. Therefore it is possible the final residual imprint left after the capacitor is fully charged to be the spiral?