# Magnetic force paradox Hall Effect

1. Jul 4, 2013

### 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

2. Jul 4, 2013

### Staff: Mentor

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

3. Jul 5, 2013

### 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.

4. Jul 6, 2013

### Staff: Mentor

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.