Can a magnetic field exist without an electric field present?

I know an electric field can exist without a magnetic field as in the case where you have a stationary point charge.

But, magnetic fields are created by moving charges so wouldn't you always need an electric field to have a magnetic field? Even in the case of permanent magnets, from what I know, it's the aligned moving electrons in the atoms of the material which cause the magnetic properties so doesn't that mean there's always an electric field in order to have a magnetic field?

• Electrostatics + relativistic transformations = magnetism as shown here damtp.cam.ac.uk/user/db275/concepts/EM.pdf – Farcher Jun 26 '18 at 7:18
• „I know an electric field can exist without a magnetic field as in the case where you have a stationary point charge.“ that is wrong Electrons, protons and even neutrons have a magnetic dipole moment. And magnetic fields could be made by the alignment and self-holding of the electrons (or even the protons) magnetic dipole moments. – HolgerFiedler Jun 26 '18 at 18:50
• A stationary point charge, what is that? How can anything be stationary in the universe? All motion, and position is relative. For an observer that is moving relative to the point charge, will certainly feel its magnetic field. Is the point charge static and has no magnetic field, or is it moving and has? Whether or not something is an electric or magnetic field is not a property that can be exclusively determined across all observers. They are aspects of the same thing. – Stian Yttervik Jun 27 '18 at 5:54

The "magnetic field" is a concept within classical electrodynamics. Maxwell's equations were developed in the mid 19th century at a time where basic atomic physics was still a nascent field of study.

Viewed in the contemporary historical context, a permanent magnet is a perfectly fine example of a magnetic field without an electric field. Within the theory of classical electrodynamics, there is no explanation for why the magnetic field exists, only that it does exist, and how it's related to the electric field. Permanent magnets have a magnetic field as an intrinsic, fundamental property, similar to the reasons rocks have mass. They just do.

In the past one and a half centuries other theories have been developed. For example the magnetic field can be explained by special relativity as length contraction apparently creating a charge imbalance, so it could be said the magnetic field doesn't exist as a fundamental property but is rather a manifestation of the electric field in moving reference frame, and quantum physics explains permanent magnets as moving charges at sub-atomic scales.

So viewed in the context of modern physics, there's really no need for a fundamental magnetic field at all since it can be explained in terms of the electric field and motion.

The discovery of a magnetic monopole would change this, but although it would bring an elegant symmetry to the kinds of particles that exist, no evidence of a magnetic monopole has been found by experiment yet.

• To be precise: permanent ferromagnets are quite often no orbital- but spin ferromagnets, i.e., moving charges are not necessary.. The story is therefore more complex as described in the video you link to. – sagittarius_a Jun 27 '18 at 21:29
• @sagittarius_a still some charge movement is involved in spin, if thought as rotation around an axis – Giorgio Pastasciutta Jun 19 at 21:22

No you can have a magnetic field without an electric field. Consider a rod with an equal number of positive and negative charges (such that they are equally spaced). Let the positive move to the left with speed $v$ and the negative to the right with speed $v$. This will result in a magnetic field but no electric field.

• So a magnetic field can exist alone if the electric field cancels? I.e. the net electric field is 0? – S H Jun 26 '18 at 7:21
• Yep exactly. Actually if you get into the details (i.e. consider relativity) for any system where you have both a magnetic and electric field you can always move into a frame (i.e change your speed) such that there is either just an electric or just a magnetic field. – Quantum spaghettification Jun 26 '18 at 7:25
• This is incorrect. If a system consists of a single charge, there is no frame without an electric field. Also in your answer you have moving charges that produce an electric field. It cancels out macroscopically, but not microscopically. Strictly speaking there is no magnetic field without an electric field unless you use approximations. – safesphere Jun 26 '18 at 9:47
• Don't the magnetic fields of the two currents cancel? – garyp Jun 26 '18 at 15:45
• @garyp No. This can be seen with the right-hand rule or more simply by the fact that you have a net current. – Quantum spaghettification Jun 26 '18 at 16:07

I suppose this is a variant of Quantum spaghettification's answer, but an obvious example is a current loop, as used in electromagnets since humans first discovered electricity.

There is no net electric field because there are equal numbers of positive and negative charges so their fields balance out. However there is a magnetic dipole due to the motion of the electrons.

• But what about the potential difference that causes the motion of electrons? – Giorgio Pastasciutta Jun 19 at 21:33

In one sense, it is an easy question, as others have pointed out. It is fairly simple to construct examples of cases with zero electric field and non-zero magnetic field.

In another sense, it's not a trivial question to answer. For example, if you see only a magnetic field in one frame, then you will see magnetic and electric field in another frame that is shifted by a change in velocity. Then there is the example of the Ahronov-Bohm effect. In this case, you have a region where both the electric and magnetic fields are zero, but an electron still feels an electromagnetic force.

The fundamental thing is the four-vector potential $A_\mu$. The electric and magnetic fields are particular arrangements of particular derivatives of this field. It is $A_\mu$ that appears in equations governing electromagnetism, such as Maxwell's equation or Dirac's equation. In several important special cases we can ignore $A_\mu$ and work with the $E_i$ and $B_i$ fields. But the fundamental understanding is always going to be based in $A_\mu$.

• Correct me if I am wrong, but I would not say that electrons "feel a force" in a zero EM fields due to the AB-effect. There is a phase shift, but macroscopically the electrons behavior is indistinguishable from there being no force. – M. Winter Jul 3 '18 at 8:43

At a fundamental elementary particle level, the answer is that as long as no magnetic monopoles are detected, then a magnetic field dipole needs a charged particle.

In atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron caused by its intrinsic properties of spin and electric charge.

There are only limits for a magnetic moment of the neutrino, a neutral particle with a very small mass. Have a look at my answer here for further links for neutrinos.

• How about the neutron? It has a magnetic dipole moment and it is magnetically alignable. – HolgerFiedler Jun 26 '18 at 18:44
• @HolgerFiedler it is not an elementary particle, it is made up of charged quarks and a magnetic moment is composite from them and their "moving" charges. – anna v Jun 27 '18 at 3:47
• Anna why I had know your answer in advance? Neutron is electrical neutral and has a spin aka a magnetic dipole moment. All other about made of quarks has to be mentioned only because the 100 years old thought about circulating currents which are the only source of magnetic field. And this is obsolet. An electron in rest - not composed off any quarks - has a magnetic dipole moment aka spin. It’s an intrinsic property. Without any movement nor revolution nor rotation of the electron. – HolgerFiedler Jun 27 '18 at 5:49
• @HolgerFiedler it happens that the quark content of the neutron is an experimental fact. The neutron is composite. My answer is about the elementary particle building blocks of the standard model. – anna v Jun 27 '18 at 7:46
• No question that the neutron is composed of quarks. My doubt is about the need of movement (acceleration) or rotation as the only source for magnetic fields. – HolgerFiedler Jun 27 '18 at 7:56

In special relativity you can show that the following are invariant quantities, i.e. they are true in all frames: $$c ^2 \mathbf{B}^2-\mathbf{E}^2, \mathbf{B}\cdot\mathbf{E}.$$

It follows that, if one frame you have non-zero electric and magnetic fields that are perpendicular (so that $$\mathbf{B}\cdot\mathbf{E} = 0$$) such that $$c^2 \mathbf{B}^2-\mathbf{E}^2 > 0$$, then it is possible to go to a frame where the electric field is zero and the magnetic field is non-zero.