A New Topic:
Magnetic Fields
P14- 1
Chapter 28 and 29
Hour 1: General introduction, Gauss’ Law
Magnetic force (28.1) Cross product of vectors.
Hour 2: Currents create B Fields: Biot-Savart,
B field of loops (magnetic moment). (28.2)
Hour 3: Use Ampere’s Law to calculate B fields (28.3)
Hour 4: Charged particle’s motion in B field. (29.1)
Hour 5: B field force & torque on wires with I (29.2)
Hour 6: Magnetic materials (29.4)
Gravitational – Electric Fields
Mass m
Create:
m
g  G r 2 rˆ
Feel:
Fg  mg
Also saw…
Charge q (±)
q
E  ke 2 r̂
r
FE  qE
Dipole p
Create:
Feel:
τ  pE
P14- 3
Magnetism – Bar Magnet
Like poles repel, opposite poles attract
P14- 4
Magnetic Field of Bar Magnet
(1) A magnet has two poles, North (N) and South (S)
(2) Magnetic field lines leave from N, enter at S
P14-
Bar Magnets Are Dipoles!
• Create Dipole Field
• Rotate to orient with Field
Is there magnetic “mass”
or magnetic “charge?”
NO! Magnetic monopoles do not exist in isolation
P14- 6
Magnetic Monopoles?
Magnetic Dipole
Electric Dipole
p
-q
q
When cut:
2 monopoles (charges)
µ
When cut: 2 dipoles
Magnetic monopoles do not exist in isolation
Another Maxwell’s Equation! (2 of 4)
Gauss’s Law
Magnetic Gauss’s Law
P14-7
Fields: Grav., Electric, Magnetic
Mass m
Create:
Feel:
g  G
r
Fg  mg
Also saw…
Create:
Feel:
m
2
Charge q (±)
rˆ
q
Ek
r̂
e
r2
FE  qE
Dipole p
E
τ  pE
No
Magnetic
Monopoles!
Dipole m
B
τ  mB
P14-8
What else is magnetic?
P14-9
Magnetic Field of the Earth
Also a
magnetic
dipole!
North magnetic pole located in southern hemisphere
P14-10
Visualization: Bar Magnet &
Earth’s Magnetic Field
(http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/27-barmagontable/27barmag320.html)
P14-11
Magnetic Field B Thus Far…
Bar Magnets (Magnetic Dipoles)…
• Create: Dipole Field
• Feel: Orient with Field
Does anything
else create or feel
a magnetic field?
P14-12
Moving Charges Feel Magnetic Force
FB  q v  B
Magnetic force perpendicular both to:
Velocity v of charge and magnetic field B
P14-13
Magnetic Field B: Units
FB  q v  B
Since
newton
N
N
B Units 
1
1
coulombmeter/second  C  m s A m
This is called 1 Tesla (T)
1 T = 104 Gauss (G)
P14-14
Recall:
Cross Product
P14-15
Notation Demonstration
X X X X
X X X X
X X X X
X X X X
OUT of page
“Arrow Head”
INTO page
“Arrow Tail”
P14-16
Cross Product: Magnitude
Computing magnitude of cross product A x B:
C  AxB
C  A B sin 
| C |: area of parallelogram
P14-17
Cross Product: Direction
Right Hand Rule #1:
1)Curl fingers of right hand
in the direction that moves A
(green vector) to B (red
vector) through the smallest
angle
2)Thumb of right hand will
point in direction of the cross
product C (orange vector)
C  AxB
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizat
ions/vectorfields/14-CrossProduct/14crossprod320.html
P14-18
Cross Product: Signs
î  ĵ  k̂
ĵ î  k̂
ĵ k̂  î
k̂  ĵ  î
k̂  î  ĵ
î  k̂   ĵ
Cross Product is Cyclic (left column)
Reversing A & B changes sign (right column)
P14-19
PRS Questions:
Right Hand Rule
P14-20
Putting it Together: Lorentz Force
FB  q v  B
Charges Feel…
FE  qE
Magnetic Fields
Electric Fields

F  q E vB

This is the final word on the force on a charge
P14-21
Application: Velocity Selector
What happens here?
P14-22
Velocity Selector
Particle moves in a straight line when
Fnet
E
 q(E  v  B)  0  v 
B
P14-23
PRS Question:
Hall Effect
P14-24