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I have searched for an answer for in what way are electric and magnetic fields perpendicular, but I only found mathematical explanations speaking of orthogonal vectors and Maxwell's equations and vector products.

I was wondering, in what sense, physically speaking, are the electric and magnetic fields perpendicular to each other?

I have seen that electromagnetism is the result of relativistic effects at the quantum level. Is it that the rotation of an electron creates these effects, and magnetic effects are related to the polar axis spin of the electron, and electric effects to the equatorial rotation of the electron? And this is why the two fields are perpendicular to each other?

And why from one frame of reference, you can see an electric field, and from another frame of reference you see a magnetic field - because it depends on your angle relative to the electron's motion?

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    $\begingroup$ What do you mean by "physically speaking"? Orthogonality is a mathematical definition. $\endgroup$ Nov 15, 2021 at 4:42
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    $\begingroup$ physics.stackexchange.com/q/61072 - hariom saranam says, "These fields are perpendicular to one another in the direction the wave is travelling." "For an electromagnetic radiation to persist the two electric and magnetic fields have to propagate in a perpendicular direction to each other" Does this mean for instance that in a propagating EM wave, from a side vantage point you will see an electric effect, and from a top vantage point you will see a magnetic effect? Or vice versa? $\endgroup$
    – Tristan
    Nov 15, 2021 at 4:53
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    $\begingroup$ That's still unclear, what do you mean by "see an electric effect" or "see a magnetic effect"? For EM waves both the electric and magnetic fields are, well, fields that have values that vary over space and time, and how they behave doesn't depend on the angle you're viewing them from. So I'm not sure what you mean by the effects depending on where your are seeing them from. $\endgroup$ Nov 15, 2021 at 4:59
  • $\begingroup$ How do they measure that you are getting an E field from one vantage point, and a B field from another? What experiment showed that this was the case? Is there some experiment where a creating an electromagnetic energy current caused electrical effects in one angle from the experiment, and magnetic effects from another angle of the experiment? What experiment originally led them to deduce that these fields were orthogonal? I was assuming that there was some experiment that resulted in simultaneous electric and magnetic effects, but in perpendicular directions, but is this assumption incorrect? $\endgroup$
    – Tristan
    Nov 15, 2021 at 5:07
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    $\begingroup$ It looks like you need to focus your question down. Note that it's fine to make multiple posts that ask distinct questions. $\endgroup$ Nov 15, 2021 at 12:21

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The electric and magnetic fields are generally not perpendicular. Presumably you're thinking of electromagnetic waves propagating in vacuum, in which case the electric and magnetic fields are perpendicular to each other and to the direction of propagation of the wave. But of course, this is not always true; in particular, it's easy to create electric and magnetic fields in the laboratory which point in whatever directions you'd like.

Beyond this, it seems like you're overthinking the issue. The electric and magnetic fields have directions associated to them, and in certain cases those directions are perpendicular to one another. There is no reason whatsoever to invoke quantum mechanics, electron spin, or relativity when talking about that fact.

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    $\begingroup$ Re "it's easy to create electric and magnetic fields in the laboratory which point in whatever directions you'd like": Yes, but you create magnetic fields generally by moving electric charges, and the resulting magnetic field then is perpendicular to both the electric field and the velocity vector. $\endgroup$ Nov 15, 2021 at 14:49
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    $\begingroup$ @Peter-ReinstateMonica Only the bit of the electric field being generated by the charge in question. If your example is occurring e.g. between two capacitor plates, or inside a Helmholtz coil, then the total electric and magnetic fields can be oriented however you wish. My reading of the OP suggests that they believe(d) that there was something fundamental about electromagnetism which causes $\mathbf E$ and $\mathbf B$ to be orthogonal to one another. $\endgroup$
    – J. Murray
    Nov 15, 2021 at 15:13
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    $\begingroup$ Well, the electrostatic field between two capacitor plates doesn't need any magnetic field, true. The relation between magnetic and electric fields is asymmetric in that the electric field is the "primary" one. But in order to have a magnetic field, you need "moving electric charges", even if that's electron spin. And I thought that the geometry of the moving electric field inside a Helmholtz coil is such that the near-homogeneous magnetic field results from that geometry, basically observing the three finger rule everywhere. But I'm not sure ;-). $\endgroup$ Nov 15, 2021 at 16:17
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    $\begingroup$ @Peter-ReinstateMonica think of the anti-Helmholtz configuration, you have zero B field at the midpoint on the axis but as you go away from the axis the field lines start to point vertically, in the same plane as the current of the coils (eg en.wikipedia.org/wiki/Biconic_cusp#/media/File:Biconic_Cusp.jpg). But I think J. Murray's point is more that you can put a capacitor in the middle of your coils such that net E and B are parallel in that region (or any arbitrary orientation between them that you want) $\endgroup$
    – llama
    Nov 15, 2021 at 17:42
  • $\begingroup$ @llama Yep, that’s precisely what I meant. $\endgroup$
    – J. Murray
    Nov 15, 2021 at 21:34
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found mathematical explanations speaking of orthogonal vectors and Maxwell's equations and vector products

This is true and these mathematical explanations are also consistent with what we find physically. If you accept that Maxwell's equations consistently describe electromagnetism and lead to electromagnetic waves (and they do), you can show that $$\bf E\cdot B=0$$ for an electromagnetic wave. That is, the $\bf B$ and $\bf E$ fields are orthogonal not only as a mathematical consequence, but this also corresponds to how they behave physically (for electromagnetic waves in a vacuum).

in what sense, physically speaking, are the electric and magnetic fields perpendicular to each other?

In the sense that the $\bf E$ and $\bf B$ fields, physically oscillate at $90^\circ$ to each other and at $90^\circ$ to the direction of propagation. That is physically how it is (again, for electromagnetic waves in space).

I have seen that electromagnetism is the result of relativistic effects at the quantum level. Is it that the rotation of an electron creates these effects, and magnetic effects are related

You do not need to go into relativity or quantum mechanics. You are adding a layer of complexity that is not needed for describing this aspect of electromagnetic waves.

Edit: As pointed out in the comments below, in the general case of electric and magnetic fields, these fields need not be orthogonal.

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    $\begingroup$ The OP is not talking of electromagnetic waves , but of general E and B fields. $\endgroup$
    – anna v
    Nov 15, 2021 at 5:47
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    $\begingroup$ The OP is talking about electromagnetic waves since he spoke about their orthogonal relationship. This is also clear by the context of the question. However, to be clear, I have added an edit to my answer. $\endgroup$
    – joseph h
    Nov 15, 2021 at 6:44
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And why from one frame of reference, you can see an electric field, and from another frame of reference you see a magnetic field - because it depends on your angle relative to the electron's motion?

No, it does not depend on the angle of motion, but on the inertial frames.

Special relativity is necessary to give the mathematical formulation.

E and B inertial frames

Lorentz boost of an electric charge.

Top: The charge is at rest in frame F, so this observer sees a static electric field. An observer in another frame F′ moves with velocity v relative to F, and sees the charge move with velocity −v with an altered electric field E due to length contraction and a magnetic field B due to the motion of the charge.

Bottom: Similar setup, with the charge at rest in frame F′.

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If there is an inertial frame where $\bf{E}=0$ (or $\bf{B}=0$), than in all other inertial frames will be either $\bf{E}=0$ (or $\bf{B}=0$), or $\bf{E} \perp \bf{B}$.

If, for instance, $\bf{B}=0$, than in this frame the charge is accelerated in the direction of $\bf{E}$. But from the other frame this dynamics is seen as combination of acceleration and rotation. This is because in Minkowski spase all that happens to vectors is either acceleration (change of energy and magnitude of spatial momentum) or rotation (change in the direction of spatial momentum).

Any acceleration (Lorentz boost) is interpreted as due to (transformed) $\bf{E}$, while the (3D) rotation is interpreted as due to (transformed) $\bf{B}$. That's why in the new frame we can see the field ($\bf{B}$ or $\bf{E}$) that was zero in the initial frame. But they will always be orthogonal due to transformation properties of the acceleration under Lorentz transformation, regardless of the properties of the sources of the fields $\bf{B}$ and $\bf{E}$.

On the pther hand, if $\bf{E} \perp \bf{B}$ and $E \neq B$, than there is an inertial frame where $\bf{E}=0$ or $\bf{B}=0$. The only case when fields are orthogonal in all frames is $\bf{E} \perp \bf{B}$ and $E = B$ (elecrtomagnetis waves in vacuum).

If the fields are not orthogonal in one frame, they will not be orthogonal in any other frame. In that case there is a reference frame where both $\bf{B}$ and $\bf{E}$ are parallel to each other, and acceleration (due to change in energy and magnitude of momentum) and centripetal (or centrifugal) force have the same direction in this frame.

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I believe the best way to visualize physically your question is in the case of the electromagnetic field of a current carrying wire conductor.

The explanation given must be fundamental and must include the dressed electron field of the bare electron's mass which is the origin and source of electromagnetism phenomenon. The discrete free electron drifting inside the wire, its electromagnetic flux envelope is cascaded with that of the other electrons inside and along the wire as illustrated below in fig.1:

fig.1

Important here is to understand shown in fig.1 that the single electron does not have separate electric and magnetic flux but a unified electromagnetic flux manifold. The electromagnetic quantum flux (i.e. EM flux of the electron quanta) of all the cascaded coherently electrons inside the current carrying wire generate the uniform macroscopic electric field inside along the wire E and magnetic B field envelope outside and along the wire. Both constitute the electromagnetic macroscopic field of the current carrying wire.

You can clearly see in the above illustration (on the right illustration of fig.1, conventional flow of current is used), that axially the electric field vector E inside the wire which is in the same direction of current I Poynting vector in the case of a current carrying wire (conventional flow of current is used), is perpendicular to the magnetic B field vectors outside the wire.

This perpendicular characteristic of the B and E components of the electromagnetic field travelling along a wire generating electric current is an inherent property of the dressed electron electromagnetic flux envelope.

On the left side of the fig.1 illustration we see the cascaded electron's field manifolds central electromagnetic flux (see horn tube flux formation diametrically on each electron manifold) clearly forming the E field inside the wire and the outside periphery electromagnetic flux of each electron manifold forming the B uniform macroscopic field outside the wire.

Notice also importantly, how the interchangeable between the electric and magnetic components nature of the electromagnetism phenomenon is demonstrated in fig.1?

The cascaded quantum flux of each electron manifold vertical segment (see diametrical horn tube formation of each manifold) which represents the magnetic moment of each electron becomes the macroscopic net electric field E inside the wire conductor and the periphery quantum flux of each electron manifold which represents the electron charge, becomes the macroscopic magnetic field B outside the wire.

The bare electron mass is positioned at the center of the dressed electron field manifold shown in fig.1, at a dimensionless point. Therefore the bare electron model is characterized by the known literature as an elementary dimensionless-point massive particle which has created in the past much confusion and non-intuitive understanding. The actual physical form of the electron particle is dressed meaning it has a charge radius.

This concludes IMO the physical explanation you particular asked in your question, besides the other more formal correct answers given.

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    $\begingroup$ I don't really know what this answer is saying but it's neither helpful nor mainstream physics. The notion of bare vs. dressed doesn't have anything to do with orthogonality of electric and magnetic fields. The answer is apparently using the term "manifold" to mean something other than its actual technical meaning, but never explaining what. "Electromagnetic quantum flux" is also not a standard technical term. $\endgroup$
    – ACuriousMind
    Nov 15, 2021 at 9:32
  • $\begingroup$ @ACuriousMind Electromagnetic quantum flux (i.e. EM flux of the dressed electron quanta). $\endgroup$
    – Markoul11
    Nov 15, 2021 at 9:51
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    $\begingroup$ @Tristan "So when the electron is described as a sphere (e.g. futurism.com/electron-edm-experiment), it is the dressed electron being described, not the bare one which is a point particle? " IMO. I don't believe they have this in mind, mainly for illustration purposes unless it is explicitly stated in the illustration. There is famous recorded speech of Dirac emphasizing the problems with the bare model of the electron mainly adopted in the literature that prevents the deeper understanding youtube.com/watch?v=GlBWe6QM23k&t=293s (listen video from that time stamp and on). $\endgroup$
    – Markoul11
    Nov 15, 2021 at 19:09
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    $\begingroup$ @Tristan "So your from figure, "E" is longitudinal the same as the current "I", and the "B" field is transverse? And this causes an electromagnetic attraction effect around the wire?" Yes that is correct, however the attraction of same current direction parallel wire to the first is only due the magnetic macroscopic field. The electric field component E is shielded inside a current carrying wire and not radiated outside. Therefore the two wires interact only magnetically and not electrostatically. For previous comment, QFT does not use the bare model of the electron. Thanks for your link. $\endgroup$
    – Markoul11
    Nov 15, 2021 at 19:21
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    $\begingroup$ Re: "an non-intuitive understanding": Do you mean "and non-intuitive understanding"? $\endgroup$ Nov 16, 2021 at 0:54

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