Magnetic force paradox Hall Effect

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Discussion Overview

The discussion revolves around the Hall effect and the implications of changing reference frames on the behavior of moving charges in a magnetic field. Participants explore the relationship between the observed Hall potential difference and the motion of the apparatus relative to the drift velocity of electrons, questioning how these factors interact in different frames of reference.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant notes that moving charges in a magnetic field experience a force, but questions what happens when the observer moves at the same velocity as the charge, suggesting that the force should be of electric nature in that frame.
  • Another participant describes two setups: one where the sample moves and the lab frame sees electrons at rest, resulting in no Hall effect, and another where the sample is at rest and electrons move, leading to the regular Hall effect.
  • A participant expresses confusion about why moving the copper strip would cause the force on the electrons to vanish, despite the expectation of a new electric force arising to maintain the Hall potential.
  • Another participant clarifies that field transformations occur only with a change in reference frame, asserting that the motion of the strip does not affect the analysis in the lab frame where no electric component exists.

Areas of Agreement / Disagreement

Participants express differing views on the implications of reference frame changes for the Hall effect, with some asserting that the motion of the apparatus alters the observed forces while others maintain that the fundamental physics remains consistent across frames. The discussion remains unresolved regarding the exact nature of the forces involved in different reference frames.

Contextual Notes

The discussion highlights potential limitations in understanding the transformation of fields and forces across different reference frames, particularly in relation to the Hall effect and the conditions under which it is observed.

aayushgsa
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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
 
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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
 
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.
 
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.
 

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