Magnetic force paradox Hall Effect

[aayushgsa]

Hello,
I was taught that moving charges in an external magnetic field experience force. Okay. I wondered that if the observer was moving with the same velocity as the charge is what would happen? I studied in one book about field transformation and came to know that the charge will experience the same force but of electric nature. But recently I read about Hall effect that moving electrons with drift velocity get accumulated at one side due to external magnetic field, and a "Hall Potential difference" emerges. Okay. But it said that drift velocity can also be measured by adjusting the speed of the whole apparatus when the speed of the copper strip equals the drift velocity, the HALL POTENTIAL VANISHES. it means that in the laboratory frame the electrons get accumulated on one side but when the apparatus is move with the drift velocity, the electrons are not getting accumulated on either side. How can this happen, shouldn't the electrons experience the same force that of electric nature as in the above case, and the hall potential be the same? Is it possible that in a frame there is a potential difference but it vanishes in another frame?
Thanks

 

[mfb]

We have two different setups and two different reference frames:

Moving sample, lab frame (=electron frame): electrons are "at rest" (on average). We have no electric field (as we are in the lab frame), there is no hall effect.
Moving sample, sample frame: electrons move in the magnetic field, and we have an electric field component. Both forces cancel each other, and there is no hall effect.
Resting sample, lab frame (=sample frame): moving electrons. Just the regular hall effect due to the magnetic field
Resting sample, electron frame: we have an electric field component, and get a voltage due to that

 

[aayushgsa]

Actually my question in short language is that why by moving the copper strip the force on the electron vanishes? Despite the field transformation? There should also be a new electric force so as to maintain the Hall potential.

 

[mfb]

Despite the field transformation?

You get a transformation if (and only if) you change your reference frame. This has nothing to do with the motion of the strip. You can always analyze the system in your lab frame, where the field has no electric component.

 

[sardar]

for your question. The Magnetic Force Paradox and Hall Effect may seem contradictory at first glance, but they can be explained by the principles of relativity and electromagnetism. Let's break it down.

First, let's consider the concept of relativity. This means that the laws of physics are the same in all inertial frames of reference. In other words, the laws of physics should be the same for an observer who is moving at a constant velocity as they are for an observer who is at rest.

Now, let's apply this to the scenario you described. In the frame of reference where the observer is at rest and the charge is moving, the charge experiences a magnetic force. This is because the observer in this frame sees the charge moving through a magnetic field, which creates a force on the charge.

However, in the frame of reference where the observer is moving at the same velocity as the charge, the charge is now at rest and there is no magnetic force acting on it. This is because the observer in this frame sees the charge and the magnetic field moving at the same velocity, so there is no relative motion between them.

Now, let's consider the Hall Effect. The Hall Effect is a phenomenon where moving electrons in a conductor experience a force due to an external magnetic field, causing them to accumulate on one side of the conductor. This creates a potential difference, known as the Hall Potential, between the two sides of the conductor.

In the laboratory frame, the electrons are moving with a drift velocity due to the external magnetic field. This results in the accumulation of electrons on one side of the conductor and the emergence of the Hall Potential. However, when the apparatus is moved with the same drift velocity, the electrons are now at rest relative to the conductor and there is no longer a magnetic force acting on them. This means that there is no accumulation of electrons and the Hall Potential vanishes.

So, to answer your question, yes, it is possible for there to be a potential difference in one frame and for it to vanish in another frame. This is due to the principles of relativity and the fact that the laws of physics are the same in all inertial frames of reference. I hope this helps clarify the Magnetic Force Paradox and Hall Effect for you.