# Hall effect -- is it always applicable?

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• ktmsud
In summary, a current carrying conductor experiences a magnetic force in a magnetic field according to the equation F=BILsinθ. This force is the result of free electrons moving in the magnetic field and is strongest when the current and magnetic field are perpendicular. The force can be observed in a moving coil galvanometer and in the Hall effect, where applying a perpendicular magnetic field creates a potential difference and electric field that counter-balances the Lorentz force. The Hall voltage can also determine the sign of the charge carriers, with electrons being negative in metals. When a conductor is not fixed, the Lorentz force will cause it to move, but the electric field created by the Hall effect will maintain a stationary current in the wire. If electrons
ktmsud
TL;DR Summary
Under similar condition, why conductor experiences some net force in particular direction but in hall effect no net force is experienced. Why?
A current carrying conductor experiences magnetic force in a magnetic field.
F=BILsinθ
Where, B = Magnetic flux density
I = Current
L = Length of conductor and
θ = Angle between magnetic field and current
This force is due to free electrons moving in a magnetic field and its value is maximum when current and magnetic fields are perpendicular. [Application of this force can be seen on moving coil galvanometer]

To see hall effect, we also apply magnetic field in perpendicular direction of current. But in this case free electrons accumulate in one side of the conductor and create potential difference or electric field which gives equal but opposite force as given by magnetic field. So, force balances. In this way in hall effect net force is zero.

Am I right?
Under similar condition, why conductor experiences some net force in particular direction in one case and no net force in other?

vanhees71
Sure. A current conducting wire, which is not somehow fixed in its place, will move when a magnetic field is switched on, i.e., you have to apply other forces to keep it in a fixed position to compensate for precisely the Lorentz force on the wire due to the magnetic field you are talking about.

The Hall voltage is built up due to the motion of electrons in the wire, because of the Lorentz force. This leads to the built-up of surface charges, which lead to an electric field and corresponding forces on the electrons, which precisely counter-balance the Lorentz force on these electrons. This idea predicts correctly this Hall voltage, and the sign of this voltage also tells you whether the charge carriers are positively or negatively charged. For metals the conduction charges are electrons and thus you find out with the Hall effect that in this case these conduction charges are negative.

https://en.wikipedia.org/wiki/Hall_effect#Theory

ktmsud
vanhees71 said:
Sure. A current conducting wire, which is not somehow fixed in its place, will move when a magnetic field is switched on, i.e., you have to apply other forces to keep it in a fixed position to compensate for precisely the Lorentz force on the wire due to the magnetic field you are talking about.

The Hall voltage is built up due to the motion of electrons in the wire, because of the Lorentz force. This leads to the built-up of surface charges, which lead to an electric field and corresponding forces on the electrons, which precisely counter-balance the Lorentz force on these electrons. This idea predicts correctly this Hall voltage, and the sign of this voltage also tells you whether the charge carriers are positively or negatively charged. For metals the conduction charges are electrons and thus you find out with the Hall effect that in this case these conduction charges are negative.

https://en.wikipedia.org/wiki/Hall_effect#Theory

I always thought Lorentz force experienced by electrons inside the conductor as internal force. If their position is not fixed inside the conductor then how can they move conductor? Instead they are going to move towards one side, strike the surface and pile up there. Which will create hall voltage.

Does a conductor which is free to move always feel force in one direction and do not show hall effect at all or are there any other criteria?

The electrons are of course bound to the wire, which is connected to the battery. In the stationary state the electrons move along the wire with constant speed. If you apply a magnetic field in addition, on the moving electrons the Lorentz force is acting, which deflects them in a direction perpendicular to their velocity. This builds up surface charges on the wire. In the stationary state the force on the electrons due to the electric field due to these surface charges compensates the Lorentz force in the direction perpendicular to the velocity. So you still have the current in direction of the voltage drop due to the battery (see the figure in the Wikipedia article).

Of course, if the metal is not fixed, it starts to move due to the Lorentz force when you switch on the magnetic field. Usually this is demonstrated by experiments early on in introductory physics lectures.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/forwir2.html

ktmsud
If you do succeed in piling up the electrons on one side of your wire, you will have an electrostatic force to pull the atoms towards them, since they will be left with a net positive charge which is attracted to your pile of negative charges.

Last edited:
ktmsud
DaveE said:
If you do succeed in piling up the electrons on one side of your wire, you will have an electrostatic force to pull the atoms towards them, since they will be left with a net positive charge which is attracted to your pile of negative charges.
Okay, now I have electrostatic force to attract fixed ions. This force is internal force. Isn't it? Can internal force produce external acceleration to move wire as a whole.

vanhees71 said:
The electrons are of course bound to the wire, which is connected to the battery. In the stationary state the electrons move along the wire with constant speed. If you apply a magnetic field in addition, on the moving electrons the Lorentz force is acting, which deflects them in a direction perpendicular to their velocity. This builds up surface charges on the wire. In the stationary state the force on the electrons due to the electric field due to these surface charges compensates the Lorentz force in the direction perpendicular to the velocity. So you still have the current in direction of the voltage drop due to the battery (see the figure in the Wikipedia article).

Of course, if the metal is not fixed, it starts to move due to the Lorentz force when you switch on the magnetic field. Usually this is demonstrated by experiments early on in introductory physics lectures.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/forwir2.html
I know all these. I think I was unable to state the problem clearly.
but I found this on stackexchange, going to read the paper that answerer mentioned. THANK YOU!!!
https://physics.stackexchange.com/q...-a-current-carrying-conductor-and-hall-effect

The electrons in a crystal always sense the presence of the lattice. It is the periodicity of the lattice that allows them to flow as nearly free entities. Their momentum is not rigorously conserved: see crystal momentum. The nearly free electrons are not really free at all.

vanhees71

## What is the Hall effect?

The Hall effect is the generation of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current. It is named after Edwin Hall, who discovered it in 1879.

## Is the Hall effect applicable to all types of materials?

The Hall effect is primarily observed in conductive materials, such as metals and semiconductors. It is less commonly observed in insulators because they do not have free charge carriers to generate a Hall voltage. However, under certain conditions, even insulators can exhibit a Hall-like effect, known as the quantum Hall effect.

## Can the Hall effect be observed in non-magnetic materials?

Yes, the Hall effect can be observed in non-magnetic materials. The key requirement is the presence of a magnetic field perpendicular to the direction of the electric current. The material does not need to be inherently magnetic for the Hall effect to occur.

## Does temperature affect the Hall effect?

Yes, temperature can significantly affect the Hall effect. Changes in temperature can alter the number and mobility of charge carriers in a material, which in turn affects the Hall voltage. For example, in semiconductors, the Hall coefficient can change with temperature due to variations in carrier concentration.

## Is the Hall effect used in practical applications?

Absolutely. The Hall effect is widely used in various practical applications, including Hall effect sensors for measuring magnetic fields, current sensors, and position sensors. It is also used in the characterization of materials to determine carrier concentration and mobility.

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