Understanding the Hall Effect: Comparing Germanium and Copper Magnetometers

[Casey_Switzer]

Hey everyone, I'm a little stumped on this one, maybe someone can help.

I don't need someone to do it for me, just maybe start me in the right direction.

The American physicist E. H. Hall discovered (1979) that when a current travels along a conducting plate of width l, which is perpendcular to a magnetic field, a potential difference V appears across the plate. Prove that V = vBl

Also,

The Hall probe makes a very convenient magnetometer. Discuss the difference you might expect if the probe is made of copper in one case, where the charge carriers are negative, and germanium, where the charge carriers are positive "holes." The Hall effect reveals a difference between positive charge moving to the right and negative charge moving to the left. Explain.

Thanks for any advice you can give.

Casey

 

[gnome]

You know, I assume, that if a point particle carrying a charge q moves with velocity v through a magnetic field B and the direction of v is perpendicular to the direction of B, the particle experiences a force

F_B = qvB

in a direction perpendicular to both v and B.

Assume for the moment that the current consists of electrons flowing through the conductor.

So, imagine a conducting plate lying flat on your desk, with a current of (negative) electrons flowing through it from right to left. And imagine that there is a magnetic field directed vertically down (i.e. towards the floor) through it.

Each of the electrons is moving perpendicular to the magnetic field, & therefore experiences a force perpendicular to its direction of flow and perpendicular to the magnetic field, in the plane of the plate, away from you towards the far edge of the plate (right-hand rule applies - remember the electrons are negative). As a result, negative charges will tend to migrate away from you towards that far edge, and therefore, there will be a negative charge at that edge, and an offsetting positive charge at the edge near you (due to the "loss" of the electrons that went away).

Now you have positive charge and negative charge at opposite edges of the plate, which of course attract each other with a force that depends on the size of the charge and the distance separating them. Assume the distance is equal to the width of the plate & you can compute the magnitude of that force, and you can compute the corresponding voltage difference (the "Hall voltage") across the plate.

Equilibrium occurs when the force on the charges due to the Hall voltage is equal to the force on them due to the magnetic field.

Work on that for a while.

 

[Casey_Switzer]

Hey thanks alot! I'll do some more work on this and see how far I get.