# Does a single moving charge produce magnetic field in an empty universe?

If we have a singular charge in a universe and it is not stationary can it produce a magnetic field? Because even though it's moving there will be no relative motion and no electric force will act on it.

• Do you understand that there can be a magnetic field in a frame where a charge is moving but no magnetic field in a frame where it’s not? Why do you think relative motion and electric force are relevant to this? Commented Mar 27 at 17:09
• @Ghoster No I think even if a charge is moving it doesn't necessarily mean there will be a magnetic field because magnetic field is just electric field from another frame of referance and electric field will be created only if there is relative motion between two charges like the motion of an electron with respect to a current carrying wire. If there is no wire there will be no magnetic field even if the electron is moving. Is this correct or should I clarify more? Commented Mar 27 at 17:59
• "...and electric field will be created only if there is relative motion between two charges"... No. Electrostatic forces exist without any motion. A pure electrostatic field in one frame will transform into electric + magnetic fields in another frame. Commented Mar 27 at 18:48
• Is this correct? No. Commented Mar 27 at 19:51

It is always interesting that people do not think about the fact that an electron is not only an electric charge and therefore has an electric field, but is also a magnetic dipole and therefore always has a magnetic field.

As already indicated in the question, no statement can be made about the kinematics of a single particle in an empty universe. Acceleration simply does not exist, neither in its generation nor in its effect. However, the two intrinsic fields that each electron has as a charge and as a magnetic dipole are real.

A moving point charge always produces time dependent magnetic and electric fields according to the Maxwell equations and special relativity.

According to our current understanding of electromagnetism, a single moving charge in an empty universe would not produce a static magnetic field in the reference frame where the charge is at rest.

Here's why:

Magnetic field arises from relative motion: Magnetism is a consequence of the theory of relativity. It's not an absolute property of a single moving charge. The magnetic field is created by the relative motion between the observer and the charge. Reference frame dependence: If you are in the reference frame where the charge is stationary, you wouldn't observe a magnetic field because there's no relative motion. However, an observer in a different reference frame where the charge is moving would detect a magnetic field.

However, there's a twist:

Time-dependent magnetic field: Even in the reference frame where the charge is at rest, there can be a time-dependent magnetic field. As the charge accelerates or decelerates, a changing electric field is produced, and according to Maxwell's equations, a changing electric field creates a changing magnetic field. So, a single moving charge wouldn't produce a static magnetic field in its rest frame, but it could produce a time-dependent magnetic field during acceleration/deceleration.

• -1 It is pointless — and confusing — to describe a charge as “moving” if you are then going to consider only a reference frame in which it is not moving. Commented Mar 27 at 22:02
• This answer is wrong. Commented Mar 29 at 6:48