# Question on Hall Effect and magnetic force

• I
• dainceptionman_02
In summary: Hall voltage can be used to characterize the type of doping materialIn summary, the Hall effect is a phenomenon in which a magnetic field and a current in a conductor result in a perpendicular electric field. This effect is caused by the Lorentz force acting on charge carriers. The direction of the Hall voltage can determine the type of charge carriers present in the conductor, with the voltage being in opposite directions for positive and negative charge carriers. This can be used to characterize the type of material present in doped semiconductors.
dainceptionman_02
so with a Hall Voltage, you have positive current traveling upwards in a wire in the +y-direction and a magnetic field into the screen in the -z-direction. the right hand rule has positive charge deflecting to the left. now if you look at the drift velocity of electrons moving downward in the -y-direction, the negative of the right hand rule has the electrons deflecting to the left. if both positive and negative charge deflect to the left, then why is it assumed that there is a net negative charge on the left hand side of the wire and a positive charge on the right causing a Hall Voltage with an electric field pointing from the right to left?

with magnetic forces, the force is perpendicular to the direction of the field. if this is so, then why do permanent magnets stick together or repel in a direction that seems parallel to the direction of the field. same with solenoids or whatever creates a constant magnetic field that uses a magnet to pick up cars in the dump lot.

The force on a charge carrier is given by the Lorentz force
$$\vec{F}=q (\vec{E}+\vec{v} \times \vec{B}).$$
Now if you have a DC, then ##\vec{F}=0##, i.e., the electric field is given by
$$\vec{E}_{\text{perp}}=-\vec{v} \times \vec{B}.$$
Now you have the driving voltage such that
$$\vec{j}=q v \vec{e}_y, \quad q v>0.$$
If now ##q>0## you have thus ##v>0## and thus (according to your description)
$$\vec{E}_{\perp}=-v B \vec{e}_y \times (-\vec{e}_z)=v B \vec{e}_x,$$
i.e., the potential is
$$V_{\text{H}}=-v B x.$$
If ##q<0##, then ##v<0## and thus
$$\vec{E}_{\text{perp}}=-v B \vec{e}_x,$$
i.e., the Hall voltage is
$$V_{\text{H}}=+v B x,$$
i.e., it's in the opposite direction as if the charge carriers are positive. Thus, with the Hall effect you can check, whether the conducting particles are positive or negative. For usual metallic conductors these are electrons and thus negatively charged. In some semiconductors the conduction is due to the motion of positively charged "quasiparticles", i.e., "missing electrons"/"holes", and for them the Hall voltage is opposite than in metallic conductors.

SammyS
If you have both types of carriers they have different drift velocities (different mobilities) so the Hall voltages don't cancel out even if they have the same concentration. In doped semiconductors they have both different concentrations and different mobilities

Last edited:
vanhees71

## 1. What is the Hall Effect?

The Hall Effect is a phenomenon in which a magnetic field applied perpendicular to the direction of current flow in a conductor causes a voltage difference across the conductor. This voltage difference is known as the Hall voltage and is directly proportional to the strength of the magnetic field.

## 2. How does the Hall Effect work?

The Hall Effect works by the interaction between a magnetic field and the moving charges (electrons) in a conductor. When a magnetic field is applied perpendicular to the direction of current flow, the electrons experience a force known as the Lorentz force. This force causes the electrons to move to one side of the conductor, creating a voltage difference.

## 3. What is the significance of the Hall Effect?

The Hall Effect is significant because it allows for the measurement of magnetic fields. By measuring the Hall voltage, the strength of a magnetic field can be determined. The Hall Effect is also used in various applications, such as in sensors and electronic devices.

## 4. What is the difference between the Hall Effect and magnetic force?

The Hall Effect is a specific phenomenon that occurs in conductors when a magnetic field is applied perpendicular to the direction of current flow. It results in the generation of a voltage difference. On the other hand, magnetic force is a general term that refers to the force exerted by a magnetic field on a moving charge or another magnet. The Hall Effect is a type of magnetic force.

## 5. How is the Hall Effect used in practical applications?

The Hall Effect is used in a variety of practical applications, such as in sensors for measuring magnetic fields, in electronic devices for detecting current flow, and in magnetic data storage. It is also used in the study of materials, such as determining the type and concentration of charge carriers in a material.

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