Biot Savart Law and Einstein’s Moving Conductor Problem

By Johny Jagannath

I contend that there is a misunderstanding here with regard to the Biot Savart law and Lorentz force. Einstein claimed in his “problem” that a moving conductor near a magnet with a field B experiences a force depending on the frame of reference.

Scenario: A conductor with moving charges in it moves relative to a permanent magnet with field B. (We don’t know which is moving because it is all relative.)

Firstly, from the frame of reference of the magnet: The magnet is stationary. The charges that are moving in the wire see cut the field of the magnet B and experience a Lorentz force given by: qvB where q is the moving charge, v is the relative velocity between the charge and the magnetic field B (B is the field of the permanent magnet).

Now from the frame of reference of the charge or the conductor: The wire is stationary. The charges are moving in the wire, but the magnet with field B is moving relative to the wire with a relative velocity of v. Therefore, the charges experience a Lorentz force given by: qvB because nothing has changed but the conductor is not moving,

From the above we see that the charges in the wire experience the same force regardless of the frame in the above scenario.

BIOT SAVART LAW

In the scenario proposed by Einstein the Biot Savart law is crucial. The law says that a magnetic field is produced by a moving charge in a wire (or conductor). Some like Feynman have argued that in the frame of the wire there are moving charges that produce the magnetic field B. And then they say, if we consider the reference frame of the charges, the charges are stationary and therefore there should not be a magnetic field in the wire.

But this is incorrect, since if we consider the charges (electron) as stationary, then the protons in the wire are moving backward relative to the charges (electrons). Since a proton is particle with a positive charge, the wire would still produce a magnetic field which is contrary to mainstream view. 

The mainstream view stipulates that if the charges are considered stationary, nothing in the wire produces a magnetic field. I just challenged that and showed that particles are still moving but they are protons in the opposite direction of the charges. Hence a magnetic field is produced in the wire regardless of the frame of reference.

Therefore there is a misunderstanding here about the Biot Savart law and Einstein’s moving conductor in a magnetic field problem. 

Feynman observed this about moving charges (presumably in a wire or in a tube with low pressure gas or air).

Richard Feynman – Lecture

http://www.feynmanlectures.caltech.edu/II_01.html#Ch1-S5

An observer who was riding along with the two charges, however, would see both charges as stationary, and would say that there is no magnetic field.

I would respond to Feynman saying, that two moving charges in empty space cannot produce a magnetic field. There is no experiment that supports this claim. However, two charges moving in a wire can produce a magnetic field. 

If we then consider the two charges are stationary, then the protons in the wire with positive charge would be moving in the opposite direction, that will result in a magnetic field. Hence the notion that there can be no magnetic field when charges move in a wire is patently wrong.

I looked up experiments on Grok and found no experiment that supports that idea that two charges moving in empty space can produce a magnetic field. The experiments found in relation to this Einstein scenario or Biot Savart law suggest that some medium is needed for the charges to flow in, in order for a magnetic field to be generated. 

Hence I claim that Feynman and Einstein appear to be incorrect in their assertions and are saying things that are not proven by experiment.