The Hall effect and the magnetic force on current carrying wires

[dak246]

As I understand it, a current flowing through a conducting strip in a magnetic field perpendicular to the current will drift to the side creating an electric field that corrects the currents motion and creates a potential difference across the conductor. Why then does a current carrying wire in the same magnetic field "bend" to the side? According to the hall effect wouldn't the wires path not be self corrected? If the charge carriers move to one side creating an electric field, wouldn't the charge carriers be pulled back, leaving only a potential difference but no change in shape of the wire because the forces of the magnetic and electric fields would cancel? My only thought is that its a matter of flexibility of the conductor, but would this then imply that a flexible wire in a magnetic field doesn't experience a hall potential difference, rather it just bends?

 

[Doc Al]

In both cases there will be a sideways force on the current carrying "wire", regardless of its shape. Whether the wire bends or not depends on its rigidity, just as you suspect.

Take a normal copper wire as an example. The moving electrons are pushed to one side until the electric and magnetic forces balance. But now the separated charges exert an electric force on the positive lattice of the wire (one side has a positive charge due to missing electrons). No matter how you slice it, the force on the current-carrying wire remains.

Make sense?

 

[dak246]

Let me make sure I understand completely...The magnetic field force inside the wire is balanced by the resulting electric field force, which "straightens out" the current, but the magnetic field force is still acting externally on the wire as a whole with no force acting to balance it? Therefore there will always be a force acting on the conductor, but whether or not it moves is a matter of its flexibility?

 

[Doc Al]

Let me make sure I understand completely...The magnetic field force inside the wire is balanced by the resulting electric field force, which "straightens out" the current,

I don't know what you mean by "straightens out". The moving charges (lets say electrons, for example) drift to the side due the magnetic field. As the charge builds up on one side, the electric field due the remaining positively charge conductor exerts a force that exactly balances the magnetic force on the moving current. Of course, the built up negative charge exerts an equal and opposite force on the positive lattice: this force is exactly equal to the magnetic force on the moving charges.

but the magnetic field force is still acting externally on the wire as a whole with no force acting to balance it?

In effect, yes: A force equal to the magnetic force acts on the wire. But it's not really the magnetic force directly, since the magnetic force acts only on the moving charges, and we know that the net force on the moving charge is zero.

Therefore there will always be a force acting on the conductor, but whether or not it moves is a matter of its flexibility?

Right!

 

[dak246]

I think I'm mostly confused about the drift of the current. Is the moving current in essence not drifting to either side at all because the forces on it cancel? If it is drifting then I'm not sure I understand the Hall effect, as I would think the forces due to the fields would cancel each out inside the conductor.

And for the bending of the conductor, can the force that bends it can be thought of as the summation of the individual forces acting on each moving charge inside it?

 

[Doc Al]

I think I'm mostly confused about the drift of the current. Is the moving current in essence not drifting to either side at all because the forces on it cancel? If it is drifting then I'm not sure I understand the Hall effect, as I would think the forces due to the fields would cancel each out inside the conductor.

Realize that the transverse electric field is due to the sideways shifting of the charge carriers.

Imagine a current carrying wire with no magnetic field. Is there a transverse electric field acting on the moving current? No.

Now apply the magnetic field. The moving charge will experience a transverse magnetic force. The charges will move sideways until the resultant electric field (due to the charge build up on the sides of the conductor) balances the magnetic field. One side of the wire is positive while the other is negative. (If the charges didn't move sideways, there would be no electric field produced.)

And for the bending of the conductor, can the force that bends it can be thought of as the summation of the individual forces acting on each moving charge inside it?

If you include forces due to all the fields (magnetic and electric) on all the charges (not just the moving ones). This net bending force will be equal to the magnetic force on the moving charges.

 

[dak246]

Ok that was a great explanation...its all clear now. Thanks!