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Exam 3 covers
Lecture, Readings, Discussion, HW, Lab
Exam 3 is Thurs. Dec. 3, 5:30-7 pm, 145 Birge
Magnetic dipoles, dipole moments, and torque
Magnetic flux, Faraday effect, Lenz’ law
Inductors, inductor circuits
Electromagnetic waves:
Wavelength, freq, speed
E&B fields, intensity, power, radiation pressure
Polarization
Modern Physics (quantum mechanics)
Photons & photoelectric effect
Bohr atom: Energy levels, absorbing & emitting photons
Uncertainty principle
Tues. Dec. 1, 2009
Phy208 Lect. 25
1
Current loops & magnetic dipoles
Current loop produces magnetic dipole field.
Magnetic dipole moment:
IA
current
Area of
loop
direction
magnitude
In a uniform magnetic field
Magnetic field exerts torque B, B sin
Torque rotates loop to align with B
Tues. Dec. 1, 2009
Phy208 Lect. 25
2
Works for any shape planar loop
r
IA
r
perpendicular to loop
I
Torque in uniform magnetic field
B, B sin
r r
Potential energy of rotation: U B Bcos
Lowest energy aligned w/ magnetic field
Highest energy perpendicular to magnetic field
Tues. Dec. 1, 2009
Phy208 Lect. 25
3
Question on torque
Which of these loop orientations has the largest magnitude
torque? Loops are identical apart from orientation.
(A) a (B) b (C) c
a
b
c
4
Tues.
Dec. 1, 2009
Phy208 Lect. 25
Magnetic flux
• Magnetic flux is defined
B
dA
B
exactly as electric flux
• (Component of B surface) x (Area element)
Faraday’s law
Time
derivative
d
B
dt
EMF around loop
Magnetic flux through
surface bounded by path
If path along conducting loop,
induces current I=EMF/R
Tues. Dec. 1, 2009
Phy208 Lect. 25
5
Quick quiz
Which of these conducting loops will have
currents flowing in them?
A.
C.
I(t) increases
Constant I
B.
Constant v
Constant I
Tues. Dec. 1, 2009
D.
Constant v
Constant I
Phy208 Lect. 25
6
Lenz’s law & forces
• Induced current produces a magnetic field.
– Interacts with bar magnet just as another bar magnet
• Lenz’s law
– Induced current generates a magnetic field
that tries to cancel the change in the flux.
– Here flux through loop due to bar magnet is increasing.
Induced current produces flux to left.
– Force on bar magnet is to left.
Tues. Dec. 1, 2009
Phy208 Lect. 25
7
Quick Quiz
A square loop rotates at frequency f in a 1T uniform
magnetic field as shown. Which graph best
represents the induced current (CW current is
positive)?
A.
B=1T
C.
1.5
1
0.5
0
0
0
-0.5
-1
0
45 90 135 180 225 270 315 360
-1.5
0
ANGLE ( DEGREES )
45 90 135 180 225 270 315 360
ANGLE ( DEGREES )
1.5
1.5
B.
D.
1
1
0.5
0.5
0
0
0
0
-0.5
-0.5
-1
-1
-1.5
-1.5
0
45 90 135 180 225 270 315 360
ANGLE ( DEGREES )
Tues. Dec. 1, 2009
0
45 90 135 180 225 270 315 360
ANGLE ( DEGREES )
Phy208 Lect. 25
=0 in
orientation
shown
8
Lenz’s law & forces
• Induced current produces a magnetic field.
– Interacts with bar magnet just as another bar magnet
• Lenz’s law
– Induced current generates a magnetic field
that tries to cancel the change in the flux.
– Here flux through loop due to bar magnet is increasing.
Induced current produces flux to left.
– Force on bar magnet is to left.
Tues. Dec. 1, 2009
Phy208 Lect. 25
9
Quick Quiz
A person moves a conducting loop with constant
velocity away from a wire as shown.
The wire has a constant current
What is the direction of force on the loop from the wire?
A.
B.
C.
D.
E.
F.
I
Left
Ftopside Iinduced Lloop Btop ILByˆ
Right
Up
Down
v
Fbottomside Iinduced Lloop Bbottom ILByˆ
Into page
Out of page
F
F
0 cancel
leftside
Tues. Dec. 1, 2009
leftside
Btop B bottom Force is up
Phy208 Lect. 25
10
Inductors
• Flux = (Inductance) X (Current)
LI
• Change in Flux
= (Inductance) X (Change in Current)
LI
• Potential difference
dI
V L
Constant current -> no potential diff
dt
Tues. Dec. 1, 2009
Phy208 Lect. 25
11
Energy stored in ideal
inductor
• Constant current (uniform charge motion)
– No work required
to move charge through inductor
• Increasing current:
– Work VLq VL Idt
required
to move charge across induced EMF
dI
– dW VL Idt L Idt LIdI
dt
– Total work
W
I
0
Tues. Dec. 1, 2009
1 2 Energy stored
LIdI LI
in inductor
2
Phy208 Lect. 25
12
Inductors in circuits
IL t 0 0
VL t 0 Vbattery L
dIL
dt
IL
dIL Vbattery
dt
L
IL instantaneously zero, but increasing in time
IL(t)
Slope dI / dt = Vbattery / L
0
0
Tues. Dec. 1, 2009
Time ( t )
Phy208 Lect. 25
13
Just a little later…
Switch closed at t=0
IL(t)
Slope dI / dt = Vbattery / L
0
0
Time ( t )
A short time later ( t=0+Δt ), the current is increasing
…
A. More slowly
B. More quickly
C. At the same rate
Tues. Dec. 1, 2009
Phy208 Lect. 25
IL>0, and IR=IL
VR≠0, so VL smaller
VL= -LdI/dt, so dI/dt smaller
14
Electromagnetic waves
In empty space:
sinusoidal wave propagating along x with velocity
E = Emax cos (kx – t)
B = Bmax cos (kx – t)
Bmax E /c
• E and B are perpendicular oscillating vectors
•The direction of propagation is
perpendicular to E and B
Tues. Dec. 1, 2009
Phy208 Lect. 25
15
Quick Quiz on EM waves
z
c
E
Tues. Dec. 1, 2009
Phy208 Lect. 25
x
B
y
16
Power and Intensity
EM wave transports energy at its propagation speed.
Intensity = Average power/area =
2
2
2
E max Bmax E max
cBmax
co E max
I
2o
2oc
2o
2
Spherical wave: I Psource / 4 r 2
Radiation Pressure
EM wave incident on surface exerts a radiation pressure
prad (force/area)
proportional to intensity I.
Perfectly absorbing (black) surface: prad I /c
Perfectly reflecting (mirror) surface: prad 2I /c
Resulting force = (radiation pressure) x (area)
Tues. Dec. 1, 2009
Phy208 Lect. 25
17
Polarization
Linear polarization:
Linear polarizer:
E-field oscillates in
fixed plane of polarization
Transmits component of E-field parallel to
max
max
E before
cos
transmission axis E after
Absorbs component perpendicular to
transmission axis.
2
Intensity I
E max
Iafter Ibefore cos2
Circular Polarization
E-field rotates at constant magnitude
Tues. Dec. 1, 2009
Phy208 Lect. 25
18
Quantum Mechanics
• Light comes in discrete units:
– Photon energy E photon hf hc / 1240 eV nm /
• Demonstrated by Photoelectric Effect
– Photon of energy hf collides with electron in metal
– Transferssome or all of hf to electron
– If hf > (= workfunction) electron escapes
Electron ejected only if hf >
min
Minimum photon energy E photon
hf required
Tues. Dec. 1, 2009
Phy208 Lect. 25
19
Photon properties of light
• Photon of frequency f has energy hf
– E photon hf hc /
– h 6.626 1034 J s 4.14 1015 eV s
– hc 1240eV nm
• Red light made of ONLY red photons
– The intensity of the beam can be increased by
increasing the number of photons/second.
– (#Photons/second)(Energy/photon) =
energy/second = power
Tues. Dec. 1, 2009
Phy208 Lect. 25
20
Photon energy
What is the energy of a photon of red light
(=635 nm)?
A. 0.5 eV
B. 1.0 eV
1240 eV nm
E
1.95 eV
635 nm
hc
C. 2.0 eV
D. 3.0 eV
Tues. Dec. 1, 2009
Phy208 Lect. 25
21
Bohr’s model of Hydrogen atom
Planetary model:
Circular orbits of electrons around proton.
Quantization
2
r
n
ao
Discrete orbit radii allowed: n
2
Discrete electron energies: E n 13.6 /n eV
Each quantum state labeled by quantum # n
How did he get this?
Quantization of circular orbit angular mom. L r p mvr n
Tues. Dec. 1, 2009
Phy208 Lect. 25
22
Consequences of Bohr model
• Electron can make transitions
between quantum states.
• Atom loses energy: photon emitted
E photon E atomninitial E atomn final
• Photon absorbed: atom gains energy:
E photon E atomn final E atomninitial
E atom n
Tues. Dec. 1, 2009
Phy208 Lect. 25
13.6eV
n2
23
Spectral Question
Compare the wavelength of a photon produced from
a transition from n=3 to n=1 with that of a photon
produced from a transition n=2 to n=1.
A. 31 < 21
n=3
n=2
B. 31 = 21
C. 31 > 21
E31 > E21
so
E hf
hc
31 < 21
Wavelength is smaller for
larger
jump!
Tues. Dec.
1, 2009
Phy208 Lect. 25
n=1
24
Question
This quantum system (not a
hydrogen atom) has energy
levels as shown. Which photon
could possibly be absorbed by
this system?
A. 1240 nm
B. 413 nm
E photon
hc
1240 eV nm
E3=7 eV
E3=5 eV
E2=3 eV
C. 310 nm
E1=1 eV
D. 248 nm
Tues. Dec. 1, 2009
Phy208 Lect. 25
25
Matter Waves
• deBroglie postulated that matter has wavelike
properties.
• deBroglie wavelength h / p
Example:
Wavelength of electron with 10 eV of energy:
Kinetic energy
p2
E KE
p 2mE KE
2m
h
hc
1240eV nm
0.39nm
2
6
2mE KE
2mc E KE
20.51110 eV 10eV
Tues. Dec. 1, 2009
Phy208 Lect. 25
26
Heisenberg Uncertainty Principle
Using
x = position uncertainty
p = momentum uncertainty
Planck’s
constant
Heisenberg showed that the product
( x ) ( p ) is always greater than ( h / 4 )
Often write this as
x p ~
/2
h
is pronounced ‘h-bar’
2
where
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Phy208 Lect. 25
27