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It is known from $\mathbf F = q(\mathbf v \times \mathbf B)$ (magnetic part of Lorentz force law) how a magnetic field interacts with a moving charged particle.

Without going too deep into the matter, how does this field-particle interaction take place? Does the external magnetic field act directly on the particle to modify its trajectory, or must there be an interaction between the external field and the moving charge's own magnetic field, such that the resulting field (by superposition) "catapults" the particle into a modified trajectory? This is suggested by the figure below:

Catapult effect due to a wire's magnetic field within an external field

Can this catapulting effect, if it exists, appear separately from any direct field-on-particle effects? Misconceptions surrounding this topic appear to be rife, and am I seeking to clarify this definitively.

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  • $\begingroup$ Please give a reference for the picture. $\endgroup$ – my2cts Feb 9 '19 at 8:59
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The magnetic field acts directly on the charged particle.

In classical electrodynamics (which is an excellent approximation for this question), magnetic fields don't interact with each other at all — nor do electric fields, nor do electric and magnetic fields. In particular, two electromagnetic waves will pass right through each other undisturbed.

Quantum electrodynamics predicts a very weak interaction between electromagnetic waves, but it's so weak that observing it would require a lot of effort. So for all practical purposes, the fields do not interact directly with each other.

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  • $\begingroup$ So, limiting my discussion to magnetic fields, multiple fields are superpositioned but do not interact with each other, correct? In my example of a moving charged particle in an external magnetic field, the particle only 'sees' the external field and is directly affected by it, correct? That suggests any discussion of a "catapult effect" is misleading, do you agree? $\endgroup$ – M. A. Feb 9 '19 at 3:47
  • $\begingroup$ @M.A. Yes: (1) correct, (2) correct, and (3) I agree. $\endgroup$ – Chiral Anomaly Feb 9 '19 at 17:04
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In the rest frame of the particle the external magnetic field doesn't matter (since $v=0$), and it has no magnetic field. Hence, it must see an electric field caused by the Lorentz transformed external magnetic field, which accelerates it in the right direction.

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  • $\begingroup$ That makes sense, thank you. However, due to my own limitations with relativity, I do not completely follow the link to my question. Essentially, then, the particle-field interaction I described in the question is happening 'directly', since the particle is seeing an E field (Lorentz transformed external B field) in the rest frame? $\endgroup$ – M. A. Feb 9 '19 at 3:13
  • $\begingroup$ Well it sees a B field but doesn't care. As far as the particle is concerned, an E field is accelerating it. Just because a moving observer may not see an E field does not concern the particle. $\endgroup$ – JEB Feb 10 '19 at 1:17
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What are the characteristics of electric charges and of magnetic dipoles in uniform electric and magnetic fields?

  • An electric charge (a monopole) in an electric field (a dipole from separated positive and negative charges) gets attracted by the opposite charges.
  • A charge with its magnetic dipole moment in a magnetic field gets turned and by this aligned to this field. But the charge in this case doesn’t gets deflected nor accelerated towards any pole. (To be precise, such poles do not exist in the meaning, that the magnetic field lines are closed and we applying poles to the surface between a magnet and the air.)
  • A magnetic dipole never interacts with an electric field and the electric field of a charged body never interacts with a magnetic field.

But the Lorentz force exists, a moving charge gets deflected in a magnetic field. An explanation, to my knowledge, never was given. It is a phenomenon without deeper explanation.

By looking at single phenomene together, perhaps an explanation is possible. An electron obey both an intrinsic electric charge and an intrinsic magnetic dipole moment. Intrinsic means, that it exist independent from surrounding circumstances. Placing an electron into a magnetic field, the electrons magnetic dipole gets aligned with the external magnetic field. If the electron moves into this field, the alignment will be accompanied by the emission of a photon. The photon obey a moment and changes the velocity and the direction of the electron.

Seems to be, that in the case of the movement of the electron in parallel to the magnetic field the direction of the emission of the photon is also parallel to the field and the alignment is stable.

In the case, the movement of the electron is not parallel to magnetic field, the emitted photon deflects the electron and disalign the electrons magnetic dipole again. As a result of the cyclic process, the electron radiates, it’s kinetic energy gets exhausted and the spiral path is in reality a path made from tangerine slices.

All described phenomena are observed. The summarized explanation is my private opinion, which I have to underline. If there is a inconsistency in my explanation it would be great to get a comment.

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The classic effects of magnetism are fully covered by the Lorentz force. It can be confusing to try to explain them by considering field energy. If the catapult effect exists it should be possible to account for it by the Lorentz force alone.

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