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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