   Author Topic: Is proximity effect hall effect?  (Read 251 times)

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« on: June 17, 2019, 04:48:18 pm »
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/Hall.html

"If an electric current flows through a conductor in a magnetic field, the magnetic field exerts a transverse force on the moving charge carriers which tends to push them to one side of the conductor."

I'm going to say, no its not. Hall effect is from the magnetic field of the moving charge (current) interacting with the external field.

Proximity effect is the external field inducing currents in the conductor which superimpose on the existing current and create a certain current density that varies across the conductor.

Hall effect = magnetic fields interacting

Proximity effect = currents interacting

In both cases current density is altered. But they are not the same effect.

Correct?

One question might be: does hall effect have a significant impact on transformer design? ejeffrey

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« Reply #1 on: June 17, 2019, 05:03:49 pm »
Well, they are both the effect of external magnetic field on currents flowing in a conductor.  And they are both consequences of maxwells equations.  So they are both coming from the same basic physics and I am not sure you can make a sharp distinction between them.  That said, there are a number of differences in scenarios that are usually considered:

* In the proximity effect, the "external" magnetic field is thought of coming from a nearby wire, often part of the same circuit.  In the hall effect, it is usually applied externally
* In the proximity effect the important factor is the distribution of current in the offended wire.  With the hall effect we are normally concerned about the transverse emf / voltage measured across the conductor.  Of course, that EMF is what pushed the current distribution around.
* An important characteristic of the hall effect is that the charge carriers are always pushed in the same direction regardless of sign.  This means that the sign of the emf depends on the sign of the charge carrier: this is important in semiconductors where p-type semiconductors are dominated by positive charge carriers.  We don't normally care about this distinction when talking about the proximity effect.
* The hall effect is also commonly talked about in quasi 2D systems where you can get fun effects like the quantum hall effect, the Aharanov-Bohm effect, and so on.  These can't be simply related to the concepts normally considered "proximity effect"

So basically they are two different ways of thinking about the same underlying physics.

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« Reply #2 on: June 17, 2019, 05:16:52 pm »
Proximity effect is a direct consequence of Maxwell equations, more precisely of the Lenz's law they contain. In this sense "Proximity effect = currents interacting" is correct.

Hall effect is completely different physics, it comes from the Lorenz force exterted on carriers and thus depends on the type of carriers: it can be positive or negative depending on the charge of dominant carriers. The proximity effect does not depend on the type of the carriers.

Proximity effect manifests for AC currents only, Hall effet exists for DC.  "Hall effect = magnetic fields interacting" is not quite correct, I would rather say "Hall effect = carriers interacting with magnetic fields".  Note that the Hall effect depends on many microscopic parameters of the conductor which are not captured by the macroscopic EM equations:  Fermi surface geometry, electronic mean free path etc.   You can calculate the proximity effect from the Maxwell equations but to model the Hall effect you need the whole apparatus of the quantum theory of conductors... and even then it doesn't work all he time.
« Last Edit: June 17, 2019, 05:18:25 pm by pwlps »

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« Reply #3 on: June 17, 2019, 05:18:59 pm »
Proximity effect manifests for AC currents only, Hall effet exists for DC.  "Hall effect = magnetic fields interacting" is not correct, I would rather say "Hall effect = carriers interacting with magnetic fields".

Its not just the magnetic field of the moving charge interacting with the external magnetic field to result in a force that moves the charge? pwlps

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« Reply #4 on: June 17, 2019, 05:35:37 pm »
Its not just the magnetic field of the moving charge interacting with the external magnetic field to result in a force that moves the charge?

There is no interaction between fields  (at least in the classical EM theory), the interaction is between charges/currents and fields. So for the Hall effect the relevant interaction is the Lorentz force:

https://en.wikipedia.org/wiki/Lorentz_force

The qv x B part of this force, perpendicular to the main electric force, will create a sort of "skew" in the current path, generating the Hall voltage.
« Last Edit: June 17, 2019, 06:32:25 pm by pwlps »

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« Reply #5 on: June 17, 2019, 06:07:53 pm »
Note that “v” in the Lorentz equation above is the velocity of the charge carrier, which depends on the mobility in the conductor.  For a current flowing in a given (longitudinal) direction along the conductor, the transverse voltage polarity depends on the sign of the charge carrier (negative electrons in metals).  For semiconductors, the polarity depends on whether the electron or hole mobility dominates.

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« Reply #6 on: June 17, 2019, 06:54:30 pm »
The question of Hall effect vs. Maxwell equations may seem subtle but in fact it's not that complicated.
Maxwell equations tell us how the EM fields (E,B) are generated by the charge and current densities (rho, j). However, if we want to apply them to calculate the fields in a conductor they are not sufficient: we also need to add an equation telling how the current density is generated by the driving EM fields. Usually this equation is the Ohm's law: the current density is the E field multiplied by the conductivity: j=sigma*E. This is how we can model many things in conductors such as the skin effect or proximity effect.  However, the Ohm's law equation does not take into account the Hall effect. In presence of high magnetic fields we need to extend the Ohm law to take into account the term due to the Hall effect (so called "Hall conductance"). For example this term is important in magnetohydrodynamics (tokamacs, controlled fusion etc.).
« Last Edit: June 17, 2019, 07:02:16 pm by pwlps »

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« Reply #7 on: June 17, 2019, 07:11:21 pm »
Hall effect depends inversely on charge density; it's negligible in common metals.

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