Currents in Magnetic Fields Current: I qnv A d Each - - PowerPoint PPT Presentation

Currents in Magnetic Fields

• Current:

– Each charge q feels a magnetic force: – Force on a wire segment of length dl is the force

• n all of the charges in that segment:

d

I 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.

d

I 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 b c d e f

I

Hall Sensor Current Field Lines

2000 4000 6000 8000 1 10

4

• 0.2

0.2 0.4 0.6 0.8 1 10

4

2 10

4

3 10

4

4 10

4

5 10

4

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