# I Hall Voltage vs Laplace Force

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1. Jul 20, 2016

### Delta²

Ok so when we have a current carrying conductor inside a magnetic field there would be Laplace force $L\times Bi$ which is the macroscopic form of the microscopic Lorentz force $v\times Bq$ in a large number of electrons ( or it is not ???)

But also there will be hall voltage which will cancel out that microscopic Lorentz force. So wouldn't that cancel the laplace force as well??? Then how on earth do the electric motors operate???

2. Jul 20, 2016

Hall effect comes for macroscopic cases...........for if you consider one electron system, where is the hall effect???

Last edited by a moderator: Jul 21, 2016
3. Jul 21, 2016

### Delta²

The electric field from the hall voltage is $E_h=\frac{V_h}{d}$. This electric field is such as to oppose the force $v_e\times Bq_e$ so it is
$(E_h+v_e\times B)q_e=0$. ($v_e,q_e$ the drift velocity and the charge of a free electron).

4. Jul 21, 2016

### Narayanan KR

In my opinion Lorentz force is nothing but poynting energy flow E x H created by external magnetic field and varrying electric field at a nearby point because of charge moving through that point

5. Jul 21, 2016

### lychette

this is an interesting opinion....can you provide some further references or reading that will support your opinion

6. Jul 22, 2016

### Delta²

Well, not sure what Narayanan KR implies but I think I have found a solution to this that makes use of mainstream classical physics, and most specifically Newton's 3rd Law of action and reaction:

So to an electron with drift velocity $v_e$ and charge $q_e$there are being apllied two forces : The force from the electric field of hall voltage, $F_{E_h}$ and the force from the magnetic field $F_B=(v_e \times B)q_e$ and it is $F_{E_h}+F_B=0$ (1).

Now here comes the interesting part, according to the Newton's 3rd law, the electron applies a force $-F_{E_h}$ (2) to the surface charges of the conductor that create the hall voltage and the associated electric field. The force from a single electron will be negligible, but there is huge number of electrons that make up the current, and if we do the math and due to (1) and (2) we ll find that the total reaction force that the stream of electrons applies to the surface charges equals the laplace force.

(Ofcourse there is also the reaction force that the stream of electrons applies to the source of the magnetic field and it will be -Laplace force)

So what do you think of this explanation?

I guess the force that the electron stream applies to the surface charges is an internal force, thus cannot change the momentum/angular momentum of the conductor , for that is responsible the force from the magnetic field, however internal forces make the work here and are responsible for the change in kinetic energy. The Laplace force it is just another example of an external force that doesn't do work (cause magnetic field cannot do work on matter according to many threads in this forums) but is responsible for the change in momentum. (Friction is another example of such force, many threads in this forum on how friction doesn't do work on rotating wheels of a car, though it is responsible for the change in momentum).

Last edited: Jul 22, 2016
7. Jul 25, 2016

### Narayanan KR

I agree that lot of electrons moving to one side of a conductor has a macroscopic reaction effect, but my question is why at the first place that a moving electron gets deflected in a magnetic field, text books say that moving charge creates magnetic field around it and it gets attracted/repelled in an external magnetic field accordingly.
Yet i think that moving charge is not reason of magnetic field, its just change in electric field at a point creates magnetic field, just like inside a capacitor.
All we need to know clearly is what happens when we have have electric and magnetic fields perpendicular to each other in a region where a charge is placed.
We can do it by reading the papers of Heaviside or poynting available in Archives.org or conduct simple experiment with capacitors (electric field) and magnets (magnetic field) ( by creating magnetic field perpendicular to electric field in a capacitor we have to look for any electrical or EM activity )

8. Jul 26, 2016

### Delta²

How can you explain the creation of strong magnetic field from DC current then, if not because of the moving charges? Of course we know that microscopically in a DC current there is time varying electric field, but I believe that macroscopically the total electric field is nearly zero and $dE/dt$ will be almost zero. There is not strong enough $dE/dt$ term (the displacement current term in Maxwell's-Ampere's Law is very small in the case of DC current) to explain the strong magnetic field from a DC current, moving charges (the current density term in Maxwell's- Ampere's Law)is the only explanation.