Class 14: Outline
Hour 1:
Magnetic Fields
Expt. 5: Magnetic Fields
Hour 2:
Charges moving in B Fields
Exam Review
P14- 1
A New Topic:
Magnetic Fields
P14- 2
Gravitational – Electric Fields
Mass m
Create:
Feel:
G
m
g = −G 2 rˆ
r
G
G
Fg = mg
Also saw…
Charge q (±)
G
q
E = ke 2 rˆ
r
G
G
FE = qE
Dipole p
Create:
Feel:
G G G
τ = p×E
P14- 3
Magnetism – Bar Magnet
Like poles repel, opposite poles attract
P14- 4
Demonstration:
Magnetic Field Lines
from Bar Magnet
P14- 5
Demonstration:
Compass (bar magnet) in
Magnetic Field Lines
from Bar Magnet
P14- 6
Magnetic Field of Bar Magnet
(1) A magnet has two poles, North (N) and South (S)
(2) Magnetic field lines leave from N, end at S
P14- 7
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- 8
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- 9
Magnetic Monopoles?
GElectric Dipole
p
-q
q
When cut:
2 monopoles (charges)
G
µ
Magnetic Dipole
When cut: 2 dipoles
Magnetic monopoles do not exist in isolation
Another Maxwell’s Equation! (2 of 4)
G G qin
E
⋅
A
=
d
w
∫∫
S
ε0
Gauss’s Law
G G
w
∫∫ B ⋅ dA = 0
S
Magnetic Gauss’s LawP14- 10
Fields: Grav., Electric, Magnetic
Mass m
Create:
Feel:
G
m
g = −G 2 rˆ
r
G
G
Fg = mg
Also saw…
Charge q (±)
No
Magnetic
Monopoles!
Dipole p
Dipole µ
G
q
E = ke 2 rˆ
r
G
G
FE = qE
Create:
G
E→
Feel:
G G G
τ = p×E
G
←B
G G G
τ = µ×B
P14- 11
What else is magnetic?
P14- 12
Magnetic Field of the Earth
Also a
magnetic
dipole!
North magnetic pole located in southern hemisphere
P14- 13
Earth’s Field at MIT
We will measure these components
P14- 14
Experiment 5:
Bar Magnet &
Earth’s Magnetic Field
P14- 15
Visualization: Bar Magnet &
Earth’s Magnetic Field
(http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/27-barmagontable/27barmag320.html)
P14- 16
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- 17
Demonstration:
TV in Field
P14- 18
Moving Charges Feel Magnetic Force
G
G G
FB = q v × B
Magnetic force perpendicular both to:
Velocity v of charge and magnetic field B
P14- 19
Magnetic Field B: Units
Since
G
G G
FB = q v × B
N
N
newton
B Units =
=1
=1
(coulomb)(meter/second ) C ⋅ m s A ⋅ m
This is called 1 Tesla (T)
4
1 T = 10 Gauss (G)
P14- 20
Recall:
Cross Product
P14- 21
Notation Demonstration
X
X
X
X
OUT of page
“Arrow Head”
X
X
X
X
X
X
X
X
X
X
X
X
INTO page
“Arrow Tail”
P14- 22
Cross Product: Magnitude
Computing magnitude of cross product A x B:
G G G
C = AxB
G
G G
C = A B sin θ
G
| C |: area of parallelogram
P14- 23
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)
G G G
C = AxB
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizat
ions/vectorfields/14-CrossProduct/14crossprod320.html
P14- 24
Cross Product: Signs
ˆi × ˆj = kˆ
ˆj × kˆ = ˆi
ˆj × ˆi = −kˆ
ˆk × ˆj = −ˆi
kˆ × ˆi = ˆj
ˆi × kˆ = −ˆj
Cross Product is Cyclic (left column)
Reversing A & B changes sign (right column)
P14- 25
PRS Questions:
Right Hand Rule
P14- 26
Putting it Together: Lorentz Force
Charges Feel…
G
G
FE = qE
G
G
G
FB = q v × B
Electric Fields
Magnetic Fields
G
G G G
F = q E + v×B
(
)
This is the final word on the force on a charge
P14- 27
Application: Velocity Selector
What happens here?
P14- 28
Velocity Selector
Particle moves in a straight line when
G
G G G
E
Fnet = q(E + v × B) = 0 ⇒ v =
B
P14- 29
PRS Question:
Hall Effect
P14- 30
Exam Review
P14- 31