There's no gap of course; just open any textbook on electrodynamics in general and on induction motors, in particular, and study the consequences of time dependent electric and magnetic fields. ``Electrodynamics of continuous mdia'' by Landau & Lifshitz might, also, be a good place to start.

> ``Electrodynamics of continuous mdia'' by Landau & Lifshitz might, also, be a good place to start.

OK. What is actually written in Landau-Lifshitz 'Electrodynamics of continuous media', Sec. 63? That work made by the magnetic field goes to extraction of the heat.

The presence of \sigma in LL's expression means that it is not the explanation 'why the magnetic force cannot do work' because \sigma means dissipation of the energy. If we move the wire with the current in the B field we can heat the wire. But if we heat the wire being in the magnetic field it doesn't lead to the motion of the wire.

For example, in the famous experiments of Ampere when the distance between the wires changes (decreases) it leads to atppearance of the mechanical tension in the wires but not only to extraction of the heat.

So the textbooks don't contain the expression I asked.

The only true existing field strength in electrodynamics is the magnetic field strength which has a curving action or an angle effect on paths of charged bodies. Even the so called "electrostatic field strength" causes an angle by rotation as it is known from Coulomb "torsion balance" experiment where one measures only rotation angle when a positive charged body repels the other positively charged body . Nowhere one see and measure a straight repulsion or attraction between charged bodies, because also most of electromagnetic line of force between equal same charged or equal and opposite charged bodies in experiments wich are curved lines! (see for example the experimental pictures in Halliday Physics II).

Insofar electromagnetic force is only the magnetic force with a curving action on paths of charged bodies. Then

1. any stable path is by definition a curved path with two degrees of freedom (structural stability theorems).

2. There is no straight path in nature and therefore no "electrostatic force" that is believed to cause straight motion on charged bodies.

Only the traditional view according to which it must be straight paths is the background of believe on electrostatic straight action.

Of course also the related traditional view that motion is secondary and static is primary and further that the space is 3-dimensional causes misunderstanding related with the perpendikular directions between magnetic force and the original "straight" path of charged body as the background of above question.

Nevertheless if one correct all these traditional wrong standpoints related with the wrong Euclidian world view of straight lines and flat geometries and related static world view which are not measurable in experiments and are all wrong from logical point of view. And accept the reality of nature where dynamics is primary and stable paths are curved. Then one can correct the electromagnetic theory in a manner that no confusion appears as asked above. The standard Maxwell theory and books about that are incorrect and confusing, because they are based on a priori stand points of primate of static, straight world view.

I wish to add that in the experiment to measure the mechanical force, it is detected not the force but always the displacement (\delta x) of a sensor. So if one measures the magnetic force F, the experimentator must measure work W = (F * \delta x).

But if the theory states that the magnetic force does not produce work, maybe some factor is missed in the theory.

> A Quantum Theory of Magnetism by Dr. Stephan Gift

Have I asked to explain what quantum effects give the ferromagnetism, antiferromagnetism etc? No.

> The magnetic force does no work.

The magnetic force does not produce work in the case of free charges in vacuum and partly in plasma.

I asked why the magnetic force does produce work in the electric motors. And - to avoid any influence of the ferromagnetism - in the experiments of Ampere.

The fact is that quantum electrodynamics approach empirical/ experimental facts only by renormalization! Renormalization change the standard naive Maxwellian picture of electrodynamics basically and proves that standard classical and quantum electrodynamics are both basically wrong! The result is that standard believe that an electrostatic field strength exists is basically wrong! Then renormalization proves that only moving charged particles surrounded by photon fields exists which are typically for moving particles! Therefore on such moving charged particles only magnetic field strength acts which is sometimes weak and in this cases erroneously is considered according to the wrong traditional Coulomb-Maxwell picture as electrostatic field strength. Pictorially the curved path of a charged particle in magnetic field with a small curvature seems like a straight path! This becomes interpreted as the action of electrostatic force. Exact straightness does not and can not exists in nature and experiments. It is also logically impossible. Therefore electrostatic (causing straight motion for charged particles) exists only in heaven and books.

Note also that force is a physical but undefined (B. Russell in "Principles of Mathematics") name for curvature in curved motion. This is done in this way because traditionally and mistakenly one begann from primate of static and straight path or lines and try to explain retrospectively the deviation of real motions from static position and/or straight motion (Newtonian mistake). It is well known that Coulomb tried to do electromagnetism in Newton's wrong way by fabrication of a similar force. AS it is known since about 30 years by people from University of Oldenburg, Germany who tried to realize Coulomb's experiments, Coulomb's results are partly fabricated and not realizable in the claimed form under the experimental conditions in Coulomb's time (One was not able to realize the perfect electric charge shielding in Coulomb's time which was needed to measure the claimed results!)

But Coulomb did so in order to produce a similar force in electricity as Newton in gravity! Besides the logical mistakes by Newton in his force conceptions mentioned by B. Russell, the Mass as the "charge" in gravity is dimensional (1/L in geometric units) whereas the electric charge is dimensionless! Honorable colleagues have not understood this mistakes of Coulomb and Maxwell and others yet and believe religiously on correctness of Maxwell's electrodynamics.

Since elementary particles are always in stable curved motion! (in traditional speech always under action of forces). Further since for charged bodies curved motion is related with magnetic force. Therefore only magnetic force exists.

> The electric charge does the work, not the magnetic field

Could you explain how the electric charge does work in Ampere's experiments?

The point is that 1. electrostatic field strength does not and can exists at all and the only possible field and field strength is the magnetic one and 2. that no exact straight motion can be realized for any kind of particle. The rest of theory is interpretation.! So one has to accept that charged particle are moving object with a curved motion a fact that in the standard view where one believe that fields causes motion would mean electromagnetic field causes that motion.

> Maxwell's equations explain how electric charge does work :

I don't need in the explanation how the electric charge does work.

I stated the question in very clear form - how to describe mechanical work produced by the magnetic force.

If we use the wires in Ampere's experiment made of different metals, Al and Cu, and provide the equal currents in the wires for both experiments, works made by the source of the electric current (the DC battery) will be different because of different resistivity of the metals.

But works made by the magnetic forces will be the same.

This simple thought experiment explains that the E field isn't the factor which can give the effect.

> you can not uncouple the electrostatic field from the magnetic field,

I cannot uncouple the electristatic field from the magnetic field because either the electroSTATIC field exists or the magnetic field exists. These fields created by the same charge cannot coexist at the same time.

Other comments are on the same level.

> The combination of acceleration and rotation is known as Lorentz transformation.

Really? And who is the author of this outstanding discovery in the modern physics?

To clarify the questions about standard electrodynamics from theoretical point of view:

1. Maxwell theory including electrostatic/ Coulomb model (CED) is incorrect just in view of its need for its quantization or for QED. It is even from classical point of view incorrect because no experiment shows any exact straight displacement for charged bodies to support Coulomb/ Maxwell model. Only curved displacements are observable.

(For people who are interested on basic structures of physics and mathematics: both QED and CED equations and any other four dimensional model do not obey the calculus of variation (in view of their four dimensional assumption) and they are no absolute minimum solutions for variation of any action functional. But they obey the so called weak variation wich is a wrong mathematical game in view of its circulus vitiosus nature and its contradictions.)

2. QED is also incorrect in view of its need to be renormalized. Then renormalized QED is basically different than QED.

In QED one must set the time component of electromagnetic potential vector A0 zero! in order to quantize the CED into QED. This means that the time parameter as an independent dimensions must vanish from the theory. Therefore electric field strength that needs for its definition the time derivative should not exists in QED! Even if we allow the time dimension here the electric field strength can not be defined correctly as an antisymmetric tensor field because the time component of electromagnetic potential does not exists in QED!

3. It is shameful that every child learn the Maxwell's differential equations which are purely theoretical nature and have no invariant meaning, but no colleague cares the Maxwell's integral equations which are extracted directly from experimental results and have invariant character. From integral Maxwell equation one can learn the two dimensional nature of true electrodynamics in view of two dimensionality of its integrals.

One may not repeat the usual differential equations of CED without understanding their structure and meaning. These are purely theoretical constructs from which two are identities by definition (dF = (always) 0, because F = dA). Only two independent differential equations exists in CED/QED for *d* F. The field strength (curvature) F has only two degrees of freedom manifested by those of photon.

4. In my view even experimental facts reported at the beginning of this discussions prove the contradictions in the standard CED/QED interpretations of electromagnetic experiments.

Therefore one has to look for a two dimensional theory of CED and QED (with two degrees of freedom) manifested in the two degrees of freedom of photon field or magnetic field strength without electrostatic like the one formulated by me " A topological approach to quantum electrodynamics".

Dear Farhad,

You write that

> In QED one must set the time component of electromagnetic potential vector A0 zero! in order to quantize the CED into QED. This means that the time parameter as an independent dimensions must vanish from the theory.

I suggest it isn't fully so.

The problem of the modern QED is that the quantization of the scalar photons should lead to their negative energy. So Dirac, Fock and Podolsky, based on the idea of Fermi, developed a method mutually to compensate the longitudinal and scalar photons.

It gave new problem, how to create (in minds of the theoreticians) the Coulomb field. So the physicists avoided this new problem by using the Coulomb gauge.

But from the other side, the non-rellativistic QED has no problems with the quantization of the scalar photons.

Vladimir

Dear Vladimir,

the fact that one must use a gauge shows that the original model is ill concepted. The gauge is a condition on the model changing its basic structure drastically. But this logical and epistemological aspect is not understood yet because leading physicists had no idea of logic and epistemology in science and followed blindly the traditional Aristotelian-Newtonian 4D world view although there is no empirical or theoretical proof for.

(By the way with respect to "it isn't fully so":

It is fully so! Then the number of components of a vector is the same as the number of assumed dimensions of the base manifold where one consider that vector. In other words the number of components of a vector on a manifold is the representant of the number of assumed dimensions of the base manifold. Logically reduction of number of vector components is equivalent to the reduction of the base manifold dimensions. But I know logic has not enough place in physics and people follows the leader blindly even if they make basic mistakes.)

Coulomb or Lorenz gauge condition describe and show the dependencies among the assumed dimensions and reduces the number assumed dimensions in the model to number of degrees of freedom (independent dimensions) which is two in QED. This shows that the four dimensional conception of CED/QED with 4 dimensions ("four degrees of freedom") is wrong and not in agreement with experimental results. Otherwise you would not be forced to use gauge conditions!

One has to understand the geometrical meaning of a gauge condition. Then it change the geometrical structure of a model basically. The number of dimensions (degrees of freedom) in a model is such a geometrical basis of model and if it is changed by gauge condition the basis of model is changed.

The honorable colleagues do not understand yet the mathematical/geometrical meaning of gauge conditions as a linear dependency condition on the number of component of vector potential. Then algebraic or dynamical dependency as in Lorenz gauge or Coulomb gauge is a mathematical concept (like linear dependency, etc.).

The basic question is why one does not use models with degrees of freedom and use models with superficial dependent dimensions and reduce their number by gauge conditions retrospectively.

The static magnetic field does not produce work, the time-varying magnetic fields produce work, because variations in magnetic flux produce a variable electric field that is responsible for communicating mechanical work on the test charge.

> variations in magnetic flux produce a variable electric field that is responsible for communicating mechanical work on the test charge

I repeat that this is correct for the free test charges. But I asked how to write the expression for work produced by the magnetic forces in Ampere experiments for example. Obviously, the currents in his experiments were more or less constant - otherwise how he could derive his expressions for the force between the currents?

Second point.

At the beginning of XX century, when some puzzles on the design of the electric motors appeared, people measured the magnetic forces between the stator and the armature. Corresponding calculations had been made and the variable E field hadn't presented in these calculations

In thermodynamics, the expression of work due to the magnetic field depends on the material in question. For paramagnetic materials it has an expression, and for another type of material the expression varies, I don't remember the details. In the loop experiment, the magnetic work comes from the torque over the loop, the loop when rotating in an external magnetic field, produces a variation of the magnetic flux, that variation produces an electromotive force in the loop and is responsible for the work there . An additional electric field is generated inside the loop and the f.em. You have to keep the electric voltage constant. If the coil has no charge battery, a current that decays due to joule effect is produced.

Dear Farhad,

I suggest that maybe we don't need to consider the curved space (and time).

The calculations of Ampere had been generalized in the electrodynamics of Weber. His expressions describe work produced by the currents in Ampere's experiments with high accuracy.

But one little problem - there is no magnetic field in Weberian electrodynamics.

Vladimir

Dear Vladimir,

what Weber's work shows is only that the Coulomb-Maxwell Modell is ill. Nevertheless all of them are basically wrong concepted, although in view of dimensionlessness of velocity (L/t, t = L) in geometric units you can add it as Weber did to any dimensional quantity like Force without disturbing the dimensional structure of quantity. The Problem with force is that it is a component of Field strength tensor which is the electrodynamical curvature. So one has to work with field strength or U(1) curvature if one will be exact, because this curvature is a gauge invariant quantity. One should not use force although it is customary to speak about force. What Ampere, Maxwell and Weber did is the interpretation of empirical result according to their static 4D world view. But later one saw that that is not correct if one apply their models to atoms and one should quantize the models. Non of them is quantizable.

So one should decide whether one will use a general model for all electrodynamical effect including those in atoms or one will use each time a special model for each effect. In the first case which is the scientific stand point one should forget about all those traditional model because either they are not quantizable or if they are they are not understandable after renormalization. Only a two dimensional topological model like mine is correct, specially because only my model include the Lorentz force equation as an equation of motion that arise from the variation of the action functional. Non of other classical or quantized models including the QED includes Lorentz equation as equation of motion, although this force is the one directly observable in the curved motion of electrons in the magnetic field. The first term in this equation (e .E ) is just an interpretation for the case where magnetic filed is weak and one observe approximately a "straight" displacement of electrons which is in reality part of a weakly curved displacement.

> In thermodynamics, the expression of work due to the magnetic field depends on the material in question.

I explained above that work produced by the magnetic field partly goes to dissipation of the heat in the conductor (Landau & Lifshitz 'Electrodynamics of continuous media', Sec. 63). But it is part of total work. Meanwhile I asked how to describe mechanical work.

> variation produces an electromotive force in the loop and is responsible for the work there . An additional electric field is generated inside the loop and the f.em. You have to keep the electric voltage constant. If the coil has no charge battery, a current that decays due to joule effect is produced.

I repeat that Ampere measured the force produced by the constant (with time) currents - no time variables in his famous formula.

What 'additional electric current' and what f.em. were observed in Ampere's experiments?

Dear Farhad,

I don't understand from your text why Weber's model incorrectly describes the magnetostatics. Why should we complicate the consideration of the magnetostatic system by introduction of the electrodynamical curvature?

Vladimir

Dear Vladimir,

I wrote "So one should decide whether one will use a general model for all electrodynamical effect including those in atoms or one will use each time a special model for each effect." So it is up to you how you do science. But don't afraid of electrodynamic curvature. It is the same as like electrodynamic field strength. Recall my previous description of this relation. Curvature tensor is just a general and exact description of field strength tensor, etc. Also recall that electrodynamic ( magnetic) field strength causes curved motion on charged bodies! Therefore curvature tensor or short curvature.

Moreover Weber's model includes electric field strength which is defined to cause exact straight motion on electrons and charged bodies. This (exact straight) path is not given in nature, not empirically provable and also undefined mathematically in view of the necessity of infinite values to produce and defined it See my previous notes). Electric field as a filed which cause straight motions on charged bodies must be abandoned from science. There is no quantum effect caused by electric field. There is only the magnetic flux quantization caused by magnetic field strength which is a two dimensional topological invariant. Electric field has no justification in a quantum electrodynamics and hence in scientific description of electrodynamical effects at all. It is only good for

Please note my previous description.

Dear Vladimir,

I am not sure whether my previous notes were delivered correctly here in view of technical complications in pc. So I repeat the last part:

Moreover Weber's model includes electric field strength which is defined to cause exact straight motion on electrons and charged bodies. This (exact straight) path is not given in nature, not empirically provable and also undefined mathematically in view of the necessity of infinite values to produce and defined it See my previous notes). Electric field as a filed which cause straight motions on charged bodies must be abandoned from science. There is no quantum effect caused by electric field. There is only the magnetic flux quantization caused by magnetic field strength which is a two dimensional topological invariant. Electric field has no justification in a quantum electrodynamics and hence in scientific description of electrodynamical effects at all. It is only good for engineers and school teachers not for scientists.

Please note my previous description about reasons against electric field.

I verify that still some technical problems here prohibit a correct notations in both my previous notes. So I repeat all of it here.

Dear Vladimir,

I wrote "So one should decide whether one will use a general model for all electrodynamical effect including those in atoms or one will use each time a special model for each effect." So it is up to you how you do science. But don't afraid of electrodynamic curvature. It is the same as like electrodynamic field strength. Recall my previous description of this relation. Curvature tensor is just a general and exact description of field strength tensor, etc. Also recall that electrodynamic ( magnetic) field strength causes curved motion on charged bodies! Therefore curvature tensor or short curvature.

Moreover Weber's model includes electric field strength which is defined to cause exact straight motion on electrons and charged bodies. This (exact straight) path is not given in nature, not empirically provable and also undefined mathematically in view of the necessity of infinite values to produce and to define it (See my previous notes). Electric field as a filed which cause straight motions on charged bodies must be abandoned from science. There is no quantum effect caused by electric field. There is only the magnetic flux quantization caused by magnetic field strength which is a two dimensional topological invariant. Electric field has no justification in a quantum electrodynamics and hence in scientific description of electrodynamical effects at all. It is only good for engineers and school teachers not for scientists.

Please note my previous description about reasons against electric field.