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## Electromagnetic Waves

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Title: Electromagnetic Waves

1
Chapter 21
• Electromagnetic Waves

2
Exam II
Curve 30
3
Electromagnetic Waves Ch 21, Secs 812
4
James Clerk Maxwell
• 1831 1879
• Electricity and magnetism were originally thought
to be unrelated
• In 1865, James Clerk Maxwell provided a
mathematical theory that showed a close
relationship between all electric and magnetic
phenomena
• Electromagnetic theory of light

5
Maxwells Starting Points
• Electric field lines originate on positive
charges and terminate on negative charges
• Magnetic field lines always form closed loops
they do not begin or end anywhere

6
Can electric fields form closed loops?
1. Yes
2. No

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
7
Maxwells Starting Points
• A varying magnetic field induces an emf and hence
• Magnetic fields are generated by moving charges
or currents (Ampères Law)

8
Maxwells Hypothesis
• Turning Faradays Law upside down, Maxwell
hypothesized that a changing electric field would
produce a magnetic field (Maxwell-Ampères Law)

9
Maxwell Equations
closed surface enclosed charge
closed surface no mag. charge
• Conservation of energy
• Conservation of charge

Lorentz force law
10
Maxwells Predictions
• Maxwell concluded that visible light and all
other electromagnetic (EM) waves consist of
fluctuating electric and magnetic fields, with
each varying field inducing the other
• Accelerating charges generate these time varying
E and B fields
• Maxwell calculated the speed at which these
electromagnetic waves travel in a vacuum speed
of light c 3.00 x 108 m/s

11
Hertzs Confirmation of Maxwells Predictions
• 1857 1894
• First to generate and detect electromagnetic
waves in a laboratory setting
• Showed radio waves could be reflected, refracted
and diffracted
• The unit Hz is named for him

12
Hertzs Experimental Apparatus
• An induction coil is connected to two large
spheres forming a capacitor
• Oscillations are initiated by short voltage
pulses
• The oscillating current (accelerating charges)
generates EM waves

13
Hertzs Experiment
• Several meters away from the transmitter is the
• This consisted of a single loop of wire connected
to two spheres
• When the oscillation frequency of the transmitter
and receiver matched, energy transfer occurred
between them

14
Hertzs Conclusions
• Hertz hypothesized the energy transfer was in the
form of waves
• These are now known to be electromagnetic waves
• Hertz confirmed Maxwells theory by showing the
waves existed and had all the properties of light
waves (e.g., reflection, refraction, diffraction)
• They had different frequencies and wavelengths
which obeyed the relationship v f ? for waves
• v was very close to 3 x 108 m/s, the known speed
of light

15
EM Waves by an Antenna
• Two rods are connected to an oscillating 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)

16
EM Waves by an Antenna, final
• Because the oscillating charges in the rod
produce a current, there is also a magnetic field
generated
• As the current changes, the magnetic field
• The magnetic field is perpendicular to the
electric field

17
Electromagnetic Waves, Summary
• A changing magnetic field produces an electric
field
• A changing electric field produces a magnetic
field
• These fields are in phase
• At any point, both fields reach their maximum
value at the same time

18
Electromagnetic Waves are Transverse Waves
• The and fields are perpendicular to each
other
• Both fields are perpendicular to the direction of
motion
• Therefore, EM waves are transverse waves

Active Figure A Transverse Electromagnetic Wave
19
Properties of EM Waves
• Electromagnetic waves are transverse waves
• They travel at the speed of light
• This supports the fact that light is an EM wave

20
Properties of EM Waves, 2
• The ratio of the electric field to the magnetic
field is equal to the speed of light
• Electromagnetic waves carry energy as they travel
through space, and this energy can be transferred
to objects placed in their path

21
Properties of EM Waves, 3
• Energy carried by EM waves is shared equally by
the electric and magnetic fields
• Average power per unit area

22
Properties of EM Waves, final
• Electromagnetic waves transport linear momentum
as well as energy
• For complete absorption of energy U
• p U/c ? F Pave/c
• For complete reflection of energy U
• p (2U)/c ? F 2Pave/c
• Radiation pressures (forces) can be determined
experimentally

23
• This is an apparatus for measuring radiation
pressure
• In practice, the system is contained in a vacuum
• The pressure is determined by the angle at which
equilibrium occurs

24
Summary of Properties ofElectromagnetic (EM)
Waves
• They travel at the speed of light
• They are transverse waves
• E, B perpendicular to each other and velocity
• Ratio of E and B field magnitudes E/Bc
• Electric and magnetic fields carry equal energy
• They carry both energy and momentum
• Can deliver U and p to a surface

25
The Spectrum of EM Waves
• Forms of electromagnetic waves exist that are
distinguished by their frequency and wavelength
• c ƒ?
• Wavelengths for visible light range from 400700
nm
• a small portion of the spectrum
• Wavelengths
• 1 km 10-3 m (radio) electronic
• 1 ?m 10-6 m (visible, IR)
• 1 nm 10-9 m (UV, X-ray)
• 1 Å 10-10 m (X-ray) atomic
• 1 fm 10-15 m (?-ray) nuclear