From last time

1
From last time
Inductors
Flux (Inductance) X (Current)
Inductors in circuits
2
Voltage drop across inductor

• Constant current
• No voltage difference
• Current changing in time
• Voltage difference across inductor

3
RL Circuit

• Before switch closed, IL 0
• Current through inductor cannot jump
• Just after switch closed, IL 0.

• What is voltage across L just after switch closed?

• VL 0
• VL Vbattery
• VL Vbattery / R
• VL Vbattery / L

Kirchoffs loop law VR VL Vbattery R and L
in series, IL0 ?IR0, VR0
4
IL
IL instantaneously zero, but increasing in time
5
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
6
Later slope
Initial slope
What is current through inductor in equilibrium,
a long time after switch is closed?

1. Zero
2. Vbattery / L
3. Vbattery / R

Equilibrium currents not changing dIL / dt 0,
so VL0 VRVbattery IL IR Vbattery / R
IL
7
RL summary
I(t)
time constant
Switch closed at t0
8
Question

• What is the current through R1 immediately after
  the switch is closed?

1. Vbattery / L
2. Vbattery / R1
3. Vbattery / R2
4. Vbattery / (R1R2)
5. 0

IL cannot jump. IL0 just after closing
switch. All current flows through resistors.
Resistor current can jump.
9
Thinking about electromagnetism
Electric Fields
Arise from charges Capacitor, QCV
Arise from time-varying B-field Inductor, Faraday effect
Magnetic Fields
Arise from currents Inductor, FLI
Arise from time-varying E-field

• Many similarities between electricity, magnetism
• Some symmetries, particularly in time-dependence

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Maxwells unification

• Intimate connection between electricity and
  magnetism
• Time-varying magnetic field induces an electric
  field (Faradays Law)
• Time-varying electric field generates a magnetic
  field

In vacuum
This is the basis of Maxwells unification of
electricity and magnetism into Electromagnetism
11

• A Transverse wave.
• Electric/magnetic fields perpendicular to
  propagation direction
• Can travel in empty space
• f v/?, v c 3 x 108 m/s (186,000
  miles/second)

12
The EMSpectrum

• Types are distinguished by frequency or
  wavelength
• Visible light is a small portion of the spectrum

13
Sizes of EM waves

• Visible light
• typical wavelength of 500 nm 0.5 x 10-6 m
  0.5 microns (µm)

AM 1310, your badger radio network, has a
vibration frequency of 1310 KHz 1.31x106
Hz What is its wavelength?

1. 230 m
2. 0.044 m
3. 2.3 m
4. 44m

14
Quick Quiz
A microwave oven irradiates food with
electromagnetic radiation that has a frequency of
about 1010 Hz. The wavelengths of these
microwaves are on the order of A. kilometers B.
meters C. centimeters D. micrometers
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Mathematical description
x
z
y
Propagation direction
16
EM Waves from an Antenna

• Two rods are connected to an ac source, charges
  oscillate between the rods (a)
• As oscillations continue, the rods become less
  charged, the field near the charges decreases and
  the field produced at t 0 moves away from the
  rod (b)
• The charges and field reverse (c)
• The oscillations continue (d)

17
Detecting EM waves
FM antenna
AM antenna
Oriented vertically for radio waves
18
Transatlantic signals
Spark gap

• Gulgielmo Marconis transatlantic transmitter

19
Transatlantic receiver

• Left to right Kemp, Marconi, and Paget pose in
  front of a kite that was used to keep aloft the
  receiving aerial wire used in the transatlantic
  radio experiment.

20
Energy and EM Waves
Energy density in E-field
Energy density in B-field
moves w/ EM waveat speed c
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Power and intensity in EM waves

• Energy density uE moves at c

22
Example E-field in laser pointer

• 3 mW laser pointer.
• Beam diameter at board 2mm
• Intensity

• How big is max E-field?

23
Spherical waves

• Sources often radiate EM wave in all directions
• Light bulb
• The sun
• Radio/tv transmission tower
• Spherical wave, looks like plane wave far away
• Intensity decreases with distance
• Power spread over larger area

Source power
Spread over thissurface area
24
Question

• A radio station transmits 50kW of power from its
  antanna. What is the amplitude of the electric
  field at your radio, 1km away.

1. 0.1 V/m
2. 0.5 V/m
3. 1 V/m
4. 1.7 V/m
5. 15 V/m

25
The Poynting Vector

• Rate at which energy flows through a unit area
  perpendicular to direction of wave propagation
• Instantaneous power per unit area (J/s.m2 W/m2)
  is also

• Its direction is the direction of propagation of
  the EM wave
• This is time dependent
• Its magnitude varies in time
• Its magnitude reaches a maximum at the same
  instant as E and B

26
Radiation Pressure

• Saw EM waves carry energy
• They also have momentum
• When object absorbs energy U from EM wave
• Momentum ?p is transferred
• Result is a force
• Pressure Force/Area

Power
( Will see this later in QM )
Intensity
Radiation pressure on perfectly absorbing object
27
Radiation pressure force
28
Question

• A perfectly reflecting square solar sail is 107m
  X 107m. It has a mass of 100kg. It starts from
  rest near the Earths orbit, where the suns EM
  radiation has an intensity of 1300 W/m2.
• How fast is it moving after 1 hour?

1. 100 m/s
2. 56 m/s
3. 17 m/s
4. 3.6 m/s
5. 0.7 m/s