# Where does the energy come from in the potential difference in the Hall effect?

• fxdung
In summary, the potential difference in Hall effect is caused by the magnetic force, which does not do work on motion charge particles. This raises the question of where the energy comes from, but it is not a contradiction as the magnetic field can transfer energy to the electric field without doing work on matter. This is similar to other cases in physics where a force can transfer momentum without transferring energy.
fxdung
Where does energy come from in potential difference appearing in Hall effect?It is magnetic force causes this potential.But we know that magnetic force does not do work on motion charge particles, then where is the energy come from?It seems contradiction that magnetic forces cause the potential but not transfer work for charge particles.

fxdung said:
It is magnetic force causes this potential.But we know that magnetic force does not do work on motion charge particles,
The magnetic force is just part of the Hall deflection equations. How does the resulting electric field from the generated potential affect any work done? (or energy dissipated in an external Hall voltage sensing circuit)

Last edited:
vanhees71
Please explain more detail, I do not understand.

fxdung said:
Please explain more detail, I do not understand.
Can you list the full Lorentz force on a charged particle in the presence of a magnetic and an electric field?

When the Lorentz force in a Hall device causes deflection of the electrons into an external circuit, what force(s) cause the dissipated energy in the external circuit?

It's actually a good question...

anorlunda
No, I can not list the full Lorentz force!

fxdung said:
Where does energy come from in potential difference appearing in Hall effect?It is magnetic force causes this potential.But we know that magnetic force does not do work on motion charge particles, then where is the energy come from?It seems contradiction that magnetic forces cause the potential but not transfer work for charge particles.
I am not sure what you think is a contradiction. First, the B field does not decrease due to the Hall effect so why do you the B field is the source of the energy? Second, the B field cannot do work on matter, but it can transfer energy to the E field? I am just having a hard time seeing how there could be a contradiction here.

Dale said:
Second, the B field cannot do work on matter, but it can transfer energy to the E field?

Do you mean B field can transfer energy to E field without do work on matter?

fxdung said:
Do you mean B field can transfer energy to E field without do work on matter?
Yes.

But according to Maxwell theory, a varied B field can be changed to E field. But here B field is constant field,how can it transfer energy without the helping of force(work be done)?

fxdung said:
But here B field is constant field,how can it transfer energy
You have answered your own question. This is precisely my first objection listed in post 7.

This is just another case of a force that transfers momentum (##F_B=v\times B## transfers momentum to electrons thus causing separation of charges i.e the Hall voltage) but doesn't transfer energy .The most popular case of such type of forces is the friction on a car's wheels.
Usually the transfer of momentum goes along with the transfer of energy but as we see with many physics examples this is not always true.

## 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, known as the Hall voltage, across the conductor.

## 2. Where does the energy come from in the potential difference in the Hall effect?

The energy in the potential difference in the Hall effect comes from the motion of charged particles, such as electrons, in the conductor. The magnetic field causes these particles to move in a curved path, resulting in a separation of charge and the creation of a voltage difference.

## 3. Is the energy in the Hall effect derived from the magnetic field or the current?

The energy in the Hall effect is derived from both the magnetic field and the current. The magnetic field provides the force that causes the charged particles to move, while the current provides the source of these particles.

## 4. Can the potential difference in the Hall effect be controlled?

Yes, the potential difference in the Hall effect can be controlled by varying the strength of the magnetic field or the amount of current flowing through the conductor. This allows for precise measurements and applications of the Hall effect.

## 5. What are the practical applications of the Hall effect?

The Hall effect has many practical applications, including as a sensor in electronic devices to measure magnetic fields, as a method for determining the type and concentration of charge carriers in a material, and in the production of Hall effect thrusters for spacecraft propulsion.

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