Exam 3 covers Lecture, Readings, Discussion, HW, Lab

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Exam 3 coversLecture, Readings, Discussion, HW,
Lab
Exam 3 is Thurs. Dec. 3, 530-7 pm, 145 Birge
Magnetic dipoles, dipole moments, and
torque Magnetic flux, Faraday effect, Lenz
law Inductors, inductor circuits Electromagnetic
waves Wavelength, freq, speed EB fields,
intensity, power, radiation pressure Polarization
Modern Physics (quantum mechanics) Photons
photoelectric effect Bohr atom Energy levels,
absorbing emitting photons Uncertainty
principle
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Current loops magnetic dipoles

• Current loop produces magnetic dipole field.
• Magnetic dipole moment

Area of loop
current
direction
magnitude
In a uniform magnetic field
Magnetic field exerts torqueTorque rotates loop
to align with
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Works for any shape planar loop
perpendicular to loop
Torque in uniform magnetic field
Potential energy of rotation
Lowest energy aligned w/ magnetic field Highest
energy perpendicular to magnetic field
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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
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Magnetic flux

• Magnetic flux is defined exactly as electric
  flux
• (Component of B ? surface) x (Area element)

Faradays law
If path along conducting loop, induces current
IEMF/R
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Quick quiz

• Which of these conducting loops will have
  currents flowing in them?

A.
C.
I(t) increases
Constant I
B.
D.
Constant v
Constant v
Constant I
Constant I
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Lenzs law forces

• Induced current produces a magnetic field.
• Interacts with bar magnet just as another bar
  magnet
• Lenzs 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.

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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.
C.
0
0
B.
D.
0
0
?0 in orientation shown
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Lenzs law forces

• Induced current produces a magnetic field.
• Interacts with bar magnet just as another bar
  magnet
• Lenzs 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.

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Quick Quiz
A person moves a conducting loop with constant
velocity away from a wire as shown. The wire has
a constant currentWhat is the direction of force
on the loop from the wire?
I

1. Left
2. Right
3. Up
4. Down
5. Into page
6. Out of page

v
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Inductors

• Flux (Inductance) X (Current)

• Change in Flux (Inductance) X (Change in
  Current)

• Potential difference

Constant current -gt no potential diff
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Energy stored in ideal inductor

• Constant current (uniform charge motion)
• No work required to move charge through inductor
  
• Increasing current
• Work required to
  move charge across induced EMF
• Total work

Energy stored in inductor
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Inductors in circuits
IL
IL instantaneously zero, but increasing in time
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Just a little later
Switch closed at t0

• A short time later ( t0?t ), the current is
  increasing

1. More slowly
2. More quickly
3. At the same rate

ILgt0, and IRIL VR?0, so VL smaller VL -LdI/dt,
so dI/dt smaller
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Electromagnetic waves

• In empty space sinusoidal wave propagating
  along x with velocity
• E Emax cos (kx ?t)
• B Bmax cos (kx ?t)

• E and B are perpendicular oscillating vectors
• The direction of propagation is
• perpendicular to E and B

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Quick Quiz on EM waves
z
y
x
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Power and Intensity

• EM wave transports energy at its propagation
  speed.
• Intensity Average power/area

Spherical wave
Radiation Pressure
EM wave incident on surface exerts a radiation
pressure prad (force/area) proportional to
intensity I. Perfectly absorbing (black) surface
Perfectly reflecting (mirror) surface Resulting
force (radiation pressure) x (area)
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Polarization

• Linear polarization
• E-field oscillates in fixed plane of
  polarization
• Linear polarizer
• Transmits component of E-field parallel to
  transmission axis
• Absorbs component perpendicular to transmission
  axis.
• Intensity
• Circular Polarization
• E-field rotates at constant magnitude

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Quantum Mechanics

• Light comes in discrete units
• Photon energy
• Demonstrated by Photoelectric Effect
• Photon of energy hf collides with electron in
  metal
• Transfers some or all of hf to electron
• If hf gt ? ( workfunction) electron escapes

Electron ejected only if hf gt ? Minimum photon
energy required
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Photon properties of light

• Photon of frequency f has energy hf
• 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

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Photon energy

• What is the energy of a photon of red light
  (?635 nm)?

1. 0.5 eV
2. 1.0 eV
3. 2.0 eV
4. 3.0 eV

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Bohrs model of Hydrogen atom

• Planetary modelCircular orbits of electrons
  around proton.
• Quantization
• Discrete orbit radii allowed
• Discrete electron energies
• Each quantum state labeled by quantum n

How did he get this? Quantization of circular
orbit angular mom.
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Consequences of Bohr model

• Electron can make transitions between quantum
  states.
• Atom loses energy photon emitted
• Photon absorbed atom gains energy

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Spectral Question
Compare the wavelength of a photon produced from
a transition from n3 to n1 with that of a
photon produced from a transition n2 to n1.
A. ?31 lt ?21 B. ?31 ?21 C. ?31 gt ?21
E31 gt E21 so ?31 lt ?21 Wavelength is
smaller for larger jump!
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Question

• This quantum system (not a hydrogen atom) has
  energy levels as shown. Which photon could
  possibly be absorbed by this system?

E37 eV
E35 eV
A. 1240 nm B. 413 nm C. 310 nm D. 248 nm
E23 eV
E11 eV
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Matter Waves

• deBroglie postulated that matter has wavelike
  properties.
• deBroglie wavelength

Example Wavelength of electron with 10 eV of
energy Kinetic energy
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Heisenberg Uncertainty Principle

• Using
• ?x position uncertainty
• ?p momentum uncertainty
• Heisenberg showed that the product
• ( ?x ) ? ( ?p ) is always greater than ( h /
  4? )
• Often write this as
• where is pronounced h-bar

Plancksconstant