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

#### 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.

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#### berkeman

Mentor
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)

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#### fxdung

Please explain more detail, I do not understand.

#### berkeman

Mentor
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...

#### fxdung

No, I can not list the full Lorentz force!

Mentor

#### Dale

Mentor
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.

#### fxdung

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?

#### Dale

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

#### fxdung

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)?

#### Dale

Mentor
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.

#### Delta2

Homework Helper
Gold Member
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.

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

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