Maxwell’s Equations
&
Electromagnetic Waves
• We now want to explore how the principles of
Electric & Magnetic Fields lead to an
understanding of light & other electromagnetic
waves.
• The connection between EM Theory and
Optics may be a surprise.
• It was a surprise to physicists also.
Towards a complete description of EM
phenomena . . .
• The century from ~1750 to ~ 1850 saw intensive investigation of
electricity & magnetism by Coulomb, Galvani, Volta, Oersted,
Ampere, Faraday and many others.
• (You should recognize most of these names. Also, there was the
mathematician Gauss, whose theorems were crucial to the new
theory of fields.)
• Finally there was James Clerk Maxwell, a theoretician who
showed that all EM phenomena could be described by a succinct
but comprehensive theory. This theory is known as Maxwell’s
Equations.
• In addition to developing the theoretical foundation of the subject,
Maxwell was the first to recognize the connection between EM
fields and light.
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EM theory
Known phenomena
• Currents produce
magnetic field
Assumptions
• Changing magnetic field • Changing electric field is
produces electricity
equivalent to current and
(induction)
also produces magnetic field
Unification – James Clark Maxwell (1831-1879):
one field – electromagnetic (EM).
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EM wave
 
EB
 
Ev
 
Bv
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E y  E0 sin(kx  t )
B z  B0 sin(kx  t )
vx  v
E/B  v
k
2

  2f

f   v
k
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Intensity of waves
• Energy of oscillation U is
proportional to amplitude squared E2
U  E2
• Intensity – I, W/m2
energy / time power
I

area
area
• Intensity I is proportional to amplitude
squared E2, inversely proportional to r2:
IE
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1
I 2
r
1
E
r 14
How do moving charges create
magnetic fields?
• Any moving electric charge is surrounded by an
electric field and a magnetic field.
What happens when electric and
magnetic fields change?
• A changing magnetic field creates a changing
electric field.
What happens when electric and
magnetic fields change?
• A changing magnetic field creates a changing electric
field.
• One example of this is a transformer which transfers
electric energy from one circuit to another circuit.
– In the main coil changing electric current produces a changing
magnetic field
– Which then creates a changing electric field in another coil
producing an electric current
– The reverse is also true.
Making Electromagnetic Waves
• When an electric charge vibrates, the electric field
around it changes creating a changing magnetic
field.
Making Electromagnetic Waves
• When an electric charge vibrates, the electric field
around it changes creating a changing magnetic
field.
Making Electromagnetic Waves
• The magnetic and electric fields create each other
again and again.
Making Electromagnetic Waves
• The electric and magnetic fields vibrate at right
angles to the direction the wave travels so it is a
transverse wave.
Properties of EM Waves
• All matter contains charged particles that are
always moving; therefore, all objects emit EM
waves.
• The wavelengths become shorter as the
temperature of the material increases.
What is the speed of EM waves?
• All EM waves travel
300,000 km/sec in free
space. (speed of lightnature’s limit!)
• EM waves usually travel
slowest in solids and
fastest in gases.
Material
Vacuum
Speed
(km/s)
300,000
Air
<300,000
Water
226,000
Glass
200,000
Diamond
124,000
What is the wavelength &
frequency of an EM wave?
• Wavelength= distance from crest to crest.
• Frequency= number of wavelengths that pass a
given point in 1 s.
• As frequency increases, wavelength becomes
smaller.
The whole range of EM wave…
• Frequencies is called the electromagnetic
spectrum.
• Different parts interact with matter in different
ways.
• The ones humans can see are called visible light,
a small part of the whole spectrum.