Download Video: The `shape` of an electric field

Maxwell Equation 1: “Gauss’s Law”
Theory of Relativity
(Part 1)
Maxwell Equation 1: “Gauss’s Law”
Gauss’s Law expresses the fact that electric charges give rise
to electric fields.
<Video: The ‘shape’ of an electric field>
Electric fields start and stop on electric charges.
Magnetism from Spin
<Video: Bar Magnets>
Maxwell Equation 3: Ampere’s Law
Ampere’s Law expresses the fact that moving charges cause
magnetic fields. Maxwell’s contribution in unifying the four
equations that now go by the name “Maxwell’s Equations” was
to realize that changing electric fields also give rise to magnetic
fields. Three sources of magnetic fields:
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“spin”
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moving charges
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changing electric fields
Gauss’s Law expresses the fact that electric charges give rise
to electric fields.
<Video: Electric Field from Charge>
Maxwell Equation 2: “Magnetic Gauss’s Law”
The magnetic form of Gauss’s law expresses the fact that
“magnetic charges” do not exist in nature, and therefore
magnetic fields cannot be seen as coming from charges. So
only magnetic “dipoles”, that is, magnets that have both a north
and a south pole give rise to magnetic fields directly. A property
of many elementary particles is “spin”, a property that causes
these particles to act like little magnets with a north and south
pole. A so-called ferromagnet (e.g. magnetized iron) inherits its
behavior from many particles with their spins lined up.
Magnetism from Spin
<Video: Lodestone>
Magnetism from Moving Charge
<Video: Current in a Wire>
Maxwell Equation 4: Faraday’s Law
Summary of Maxwell’s contribution
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already had:
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Faraday’s law tells us the converse of the addition Maxwell
made to Ampere’s law, that changing magnetic fields give rise
to electric fields. This is the principle behind electric generators
producing electricity from mechanically rotating wires inside a
magnetic field.
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Maxwell added:
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Wave solutions of Maxwell’s Equations
electric charge generates electric field
⇒ Gauss’s Law
moving electric charge generates magnetic field
⇒ Ampere’s Law
changing magnetic field generates electric field
⇒ Faraday’s Law
no magnetic charges
⇒ Magnetic Gauss’s Law
changing electric field generates magnetic field
⇒ addition to Ampere’s Law
all together
⇒ “Maxwell’s Equations”
Waves
<Electromagnetic Waves Demo 1>
<Video: Waves on a string 1>
http://www.phys.hawaii.edu/ teb/java/ntnujava/emWave/emWave.html
<Electromagnetic Waves Demo 2>
http://www.walter-fendt.de/ph14e/emwave.htm
Waves on a Moving Chain
Waves on a String
<Video: Waves on a moving chain>
Water Waves
<Video: Water waves 1>
Water Waves
<Video: Water waves 2>
<Video: Sound waves 1>
Sound Waves
Sound Waves
<Video: Sound waves 2>
Michelson-Morley Experiment
Wave solutions of Maxwell’s equations
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The strength of the electric force is proportional to 1/4π0 ,
0 = 8.85 × 10−12 C2 /N·m2 . That is, the force between two
charges q1 and q2 is
Fcoulomb =
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<Video: Sound waves 3>
1 q1 q2
4π0 r 2
The strength of the magnetic force between two current
carrying wires is proportional to µ0 .
0 and µ0 are just properties of space
√
Maxwell found, speed of waves = 1/ 0 µ0 = c
⇒c was the already known speed of light!
doesn’t light need a medium? ⇒the “Ether”
<Michelson-Morley demo>
http://galileoandeinstein.physics.virginia.edu/more stuff/flashlets/mmexpt6.htm
Conclusion: the speed of light is the same from the point of
view of anyone, no matter what speed the perspective comes
from. Or in other words, the speed of light is the same in all
reference frames.
Waves
Summary of Einstein’s Special Relativity
1. The form of all physical laws of nature is the same in all
reference frames.
<Video: Sound and Light in a Vacuum>
2. Maxwell’s equations are laws of nature.
⇒The speed of light is the same in all reference frames.
3. A consequence: Newton’s laws must be altered for
problems with large speeds, those a sizable fraction of the
speed of light.