Currents in Magnetic Fields

• Current:

– Each charge q feels a magnetic force:

– Force on a wire segment of length dl is the force on all of the charges in that segment:

dI qnv A

B q F v B

( ) ( )dQ qn Vol qn Adl

( )

d

d

d dQ

qn Adl

I

F v B

v B

dl B

Electrostatic Equilibrium

• The charges in a conductor in electrostatic equilibrium have stopped moving.

– E = 0 throughout a conductor in electrostatic equilibrium.

Conductors in Motion (in a B field)

• Motional emf

– Drag conductor through B field at constant velocity.

– Charges rearrange until they achieve electrodynamic equilibrium

• total force on charges is zero.

Hall Effect

• Current to the left could be

– Positive charges moving to the left.

– Negative charges moving to the right.

• Applying a B field perpendicular to the current flow allows us to discriminate between these two possibilities.

dI qnv A

Figure 27.32

Hall Effect

A current I passes through a slab of metal in the presence of a magnetic field B. Between which two sides does a Hall voltage develop? Put the side with the higher potential first.

1) a and b

2) c and d

3) e and f

4) b and a

5) d and c .

B

I a bc

d

e

f

I

Hall Sensor

Current

Field Lines

0

2000

4000

6000

8000

1 104

-0.2

0

0.2

0.4

0.6

0.8

0 1 104

2 104

3 104

4 104

5 104

Magnetic Field (Oe)

Klaus von Klitzing et al., 1980 Nobel Prize: 1985

Quantum Hall Effect

Current Loop in B field

http://helios.augustana.edu/~dr/203/img/F28_20.jpg

Figure 27.22c