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I have read these questions:

Difference between electric and magnetic field (relating to EEG & MEG)

Can someone please explain magnetic vs electric fields?

Explain the origin of magnetic fields in layman terms

Mechanism by which electric and magnetic fields interrelate

where it says:

The simplest explanation I know of requires only one test charge and two reference frames with a relative velocity between them. Frame 1: The charge is at rest. It is the source of a (purely) electric field. Frame 2: The charge is moving. It is a current, and the source of a magnetic field.

Understanding the relationship between electricity and magnetism

What's the core difference between the electric and magnetic forces?

where it says:

Electric forces are created by and act on, both moving and stationary charges; while magnetic forces are created by and act on only moving charges.

Can magnetic force really be just electric force in a different frame?

Magnetic field as effect of relativity?

E field:

  1. charge is stationary to the observer

  2. monopole

  3. lines of firce radially converge

  4. easy to block

  5. mediated by virtual photons

M field:

  1. charge is moving to the observer

  2. dipole

  3. can't be blocked

  4. mediated by virtual photons

We know that electrons have E charge and M dipole moment too. But a magnet has usually no E charge.

Electric forces can act on different materials like statically charged plastics too.

Magnetic forces can usually only act on metals but not on plastics.

None of these questions says whether there is one fundamental force, the EM force, and it has different ways of acting on different materials and depending on if the charge is moving relative to the observer, or there is an electric force, and a magnetic force, and they are both mediated by virtual photons, but they act on different materials and differently depending on whether they are moving relative to the observer.

They also say that with the magnetic field, the charge is moving relative to the observer. But if you look at a magnet, it has a magnetic field, and magnetic force, and is not moving relative to the observer.

Is there a fundamental difference or is the M field/force just the E field/force in relativity (moving)?

Question:

  1. What is the fundamental difference between an E and a M field? Is it just that one is stationary the other is moving relative to the observer?

  2. Is there just one force, EM force, or is there E force and M force as they can act differently on different material? Is the M force just an E force in relativity?

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  • $\begingroup$ Related : Are magnetic fields just modified relativistic electric fields?. $\endgroup$ – Frobenius Jul 11 '18 at 10:34
  • $\begingroup$ @ Gurbir Singh you say " atomic electrons are moving around their respective nuclei constituting a dipole and the dipoles are aligned in same direction". Is the dipole not the intrinsic spin of the electron? $\endgroup$ – Árpád Szendrei Jul 11 '18 at 17:03
  • $\begingroup$ @GurbirSingh's comment is wrong. The macroscopic magnetic field of a ferromagnetic material is indeed caused by the alignment of microscopic magnetic moments, but (in ferromagnets) those atomic magnetic moments come from electron spin, not from "electrons moving around their respective nuclei". Some magnetic behaviour does indeed come from the magnetic moment caused by orbital motion, but that doesn't include ferromagnets. $\endgroup$ – Emilio Pisanty Jul 12 '18 at 11:06
  • $\begingroup$ @ Emilio Pisanty you say: " Some magnetic behaviour does indeed come from the magnetic moment caused by orbital motion, but that doesn't include ferromagnets." Can you please tell me about this some magnetic behaviour that comes from orbital motion? $\endgroup$ – Árpád Szendrei Jul 12 '18 at 16:27
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There is no fundamental difference between electric field and magnetic field.

Well, you can consider some point in space at some moment of time and measure/calculate electric field and magnetic field at this point at this moment. You would get some result: electric field is $\vec{E}$, magnetic field is $\vec{B}$. Fine, there is no ambiguity.

But if someone else who is moving according to you measures/calculates the electric and magnetic fields at the very same moment at the very same point he would get different results. Depending on his velocity the result could even be "there is no electric field" or "there is no magnetic field".

The statement "there IS an electric field at this point" may be correct or not correct depending on the frame of reference. And there is no way to tell which frame of reference is better. Generally speaking one can't tell if there is "actually" an electric field here. But it's possible to tell if there is an electro-magnetic field.

Electric and magnetic fields can't exist independently. If in one frame of reference only one of them is present in another frame both are present. So, fundamentally both of them are the same field.

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  • $\begingroup$ Thank you. You say: " measure/calculate electric field and magnetic field at this point at this moment" Can you please tell me how you can measure them? I know you can calculate them, but how do you measure them? And you say that they can't exist independently. How about a permanent magnet? That magnet is a magnet to every observer. And it does not need an electric field? $\endgroup$ – Árpád Szendrei Jul 11 '18 at 17:09
  • $\begingroup$ @ÁrpádSzendrei Magnet is a magnet to every observer - that's correct. It does not need an electric field - also correct. If the magnet is not moving it produces only magnetic field around itself. But this is correct only in your frame of reference! From the point of view of another observer this very magnet at this very moment is moving and produces both magnetic and electric fields! $\endgroup$ – lesnik Jul 11 '18 at 19:23
  • $\begingroup$ @ÁrpádSzendrei Now to the question about "how to measure the field". You can place a "probe" charge into a given point and measure the force acting on the charge. If the probe charge is not moving, it's an experimental fact that the force is proportional to charge and by definition the electric field is $\vec{E} = \vec{F}/q$. To measure the magnetic field need to measure force acting on moving probe charge and you'll find a vector $\vec{B}$ such that $\vec{F}=q * \vec{v} X \vec{B}$. $\endgroup$ – lesnik Jul 11 '18 at 19:52
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While I agree with the answer posted by lesnik, it's worth pointing out that not every magnetic field can be thought of as arising from an electric field. This isn't even true for uniform fields!

The reason is that there are two invariants of the electromagnetic field, $$E^2 - B^2 \quad \text{and} \quad \mathbf{E} \cdot \mathbf{B}$$ which don't change under Lorentz transformations. If you start with only a magnetic field, there's no way to transform it into only an electric field. We say $\mathbf{E}$ and $\mathbf{B}$ are unified because they transform freely into each other, but there are limitations. It's like how space and time are still distinct, despite being unified into spacetime; a spacelike interval cannot be transformed into a timelike one.

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  • $\begingroup$ Thank you. You say: "not every magnetic field can be thought of as arising from an electric field. This isn't even true for uniform fields" Is there an example for a magnetic field without an electric field? A permanent magnet? And do you have any answer for why a plastic can be electrostatical but not magnetized? Why do these fileds act on different material? $\endgroup$ – Árpád Szendrei Jul 11 '18 at 17:12
  • $\begingroup$ @ÁrpádSzendrei Yes, a permanent magnet's field is an example of a pure magnetic field. Hence you can't transform it into a pure electric field, though of course you can transform it into a mix of a magnetic and electric field. $\endgroup$ – knzhou Jul 11 '18 at 17:20
  • $\begingroup$ @ÁrpádSzendrei Well, for the plastic vs. magnet example, it boils down to this: a pure electric field cannot turn into a pure magnetic field and vice versa. Static charges make pure electric fields, and stationary currents make pure magnetic fields. Since the charges in plastic don't move, they make electric fields that are "more electric than magnetic", while it's just the opposite for magnets. $\endgroup$ – knzhou Jul 11 '18 at 17:21
  • $\begingroup$ You say: " Since the charges in plastic don't move, they make electric fields that are "more electric than magnetic", while it's just the opposite for magnets." What do you mean it is the opposite for magnets? So in a permanent magnet, which has no electric field, the charges are moving? $\endgroup$ – Árpád Szendrei Jul 11 '18 at 17:30
  • $\begingroup$ @ÁrpádSzendrei Well, a cheap classical model for a magnet is a permanent current moving in a loop. So there is no net charge, but there is current. I didn't say that explicitly because to really explain a permanent magnet you need quantum effects, but this would apply for, e.g. an electromagnet. $\endgroup$ – knzhou Jul 11 '18 at 17:32
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I have asked myself this same question. The answer is that the electric force and the magnetic force are ultimately different things.

When physicists refer to the electromagnetic force as being a single force, what they really should be saying is that we have a single set of equations (the Maxwell equations) that describe both of them together.

At the level of Quantum Electrodynamics, both the electric field and the magnetic field are mediated by exchange of virtual photons. However, the "virtual photon" model doesn't really resolve the issue of whether the electric field and magnetic field are the same thing. The virtual photon exchange is really just something that we calculate to determine scattering cross sections.

I realize that in this answer, I haven't really justified how I know that electric fields and magnetic fields are different things. But I suppose the burden of proof is on those who are saying that they are fundamentally the same thing.

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The answer is that neither the electric field alone nor the magnetic field alone can be considered the central item here. Rather, they are two parts---two vector fields---which together form the field tensor or Faraday tensor. This is a second-rank tensor; if you are unfamiliar with it, note mainly that it can be written down as a 4 by 4 matrix and the field equations can be written in terms of it, as can the equation for the force on a charged particle. The field tensor is what it is. Its relation to different reference frames can be compared to the relation between a vector and coordinate axes. A given vector, such as a force or something like that, will have components that depend on what directions in space you choose when setting up the coordinate system, but it is still the same force and the same vector when you change from one coordinate system to another, even though the components then change. In a comparable way, the second-rank tensor describing the electromagnetic field is what it is, independent of inertial reference frame, but its components express what form it takes in any given reference frame. That form may be electric or magnetic or both, depending on circumstances.

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