Maxwell’s Equations
and Electromagnetic Waves
4/9/2015
Kevin Holway
Maxwell's Equations
Galilean field transformations
Maxwell’s equations
Electromagnetic waves
Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, 1890.
Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:James_Clerk_Maxwell.png#/media/File:James_Clerk_Maxwell.png
Maxwell's Equations
Galilean field transformations
Maxwell’s equations
Electromagnetic waves
Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, 1890.
Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:James_Clerk_Maxwell.png#/media/File:James_Clerk_Maxwell.png
Sharon runs past Bill while
holding a positive charge q.
In Bill’s reference frame,
the charge creates
A. Only an electric field.
B. Only a magnetic field.
C. An electric and a magnetic field.
D. No fields.
Sharon runs past Bill while
holding a positive charge q.
In Sharon’s reference frame,
the charge creates
A. Only an electric field.
B. Only a magnetic field.
C. An electric and a magnetic field.
D. No fields.
Galilean transformations
and Galilean invariance
Sharon runs past Bill while
holding a positive charge q
through a uniform, constant
magnetic field that Bill created.
Then Bill measures a force
on Sharon’s charge that is:
A. Zero
B. Non-zero
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Sharon runs past Bill while
holding a positive charge q
through a uniform, constant
magnetic field that Bill created.
Then Sharon measures a force
on her charge that is:
A. Zero
B. Non-zero
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Experimenters on earth have
created the magnetic field
shown. A rocket flies through
the field, from right to left.
Which are the field (or fields)
in the rocket’s reference frame?
Not quite relativity…
Maxwell's Equations
Galilean field transformations
Maxwell’s equations
Electromagnetic waves
Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, 1890.
Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:James_Clerk_Maxwell.png#/media/File:James_Clerk_Maxwell.png
The equations so far
and displacement current
The electric field is decreasing.
Which is the induced magnetic field?
E. There’s no induced field in this case.
Example: induced magnetic field
in a discharging capacitor
Maxwell's equations
Along with Lorentz force law, this is the fundamental content
of classical electromagnetic theory
Maxwell's equations in vacuum
Maxwell's equations in vacuum
(differential form)
Maxwell's Equations
Galilean field transformations
Maxwell’s equations
Electromagnetic waves
Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, 1890.
Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:James_Clerk_Maxwell.png#/media/File:James_Clerk_Maxwell.png
"We can scarcely avoid the
conclusion that light consists in
the transverse undulations of the
same medium which is the cause
of electric and magnetic
phenomena."
Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, 1890.
Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:James_Clerk_Maxwell.png#/media/File:James_Clerk_Maxwell.png
Prediction by Maxwell: Propagating Wave
With Speed of Light c
Sinusoidal plane wave
<get better animation>
Demo: sources and linearly polarized light
(dipole antenna)
http://www2.lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSpec2.html
How is light created?
Accelerating charges
Img at right: "Black body" by Darth Kule - Own work. Licensed under Public Domain via Wikimedia Commons http://commons.wikimedia.org/wiki/File:Black_body.svg#/media/File:Black_body.svg
How is light created?
Quantum mechanical processes
How is light created?
Cerenkov radiation
Demo: Spectra
(gas discharge tubes and diffraction gratings)
http://www2.lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSpec2.html
Wavelength determines color
but color does not determine wavelength!
Color is a complex perception
of the world
constructed by your brain.
Why are living creatures tuned
to the visual spectrum?
Sun emits the most energy in visual range of spectrum (Stefan-Boltzmann law).
Water vapor in atmosphere blocks most light except the visual range.
Maxwell's Equations
Galilean field transformations
Maxwell’s equations
Electromagnetic waves
Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, 1890.
Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:James_Clerk_Maxwell.png#/media/File:James_Clerk_Maxwell.png
"Mantis shrimp from front" by Jenny - originally posted to Flickr as mantis shrimp. Licensed under CC BY 2.0 via Wikimedia Commons http://commons.wikimedia.org/wiki/File:Mantis_shrimp_from_front.jpg#/media/File:Mantis_shrimp_from_front.jpg