Download Electromagnetic Waves

Chapter 34
Electromagnetic Waves
Copyright © 2009 Pearson Education, Inc.
Chapter 34: Electromagnetic Waves
Copyright © 2009 Pearson Education, Inc.
Chapter Outline
1. Changing Electric Fields
Produce Magnetic Fields
2. Modification of Ampère’s Law
Maxwell’s Displacement Current
3. Gauss’s Law for Magnetism
Maxwell’s Equations
• Production of Electromagnetic Waves
• Electromagnetic Waves, & Their Speed
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Derived from Maxwell’s Equations:
1. Light as an Electromagnetic Wave
2. The Electromagnetic Spectrum
3. Measuring the Speed of Light
4. Energy in Electromagnetic Waves
The Poynting Vector
Radiation Pressure
Radio & Television
Wireless Communication
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Changing Electric Fields Produce Magnetic
Fields: Ampère’s Law & Displacement Current
Maxwell’s Generalization of Ampère’s Law
Consider a wire carrying a
Recall Ch. 30 Ampère’s Law:
Current I
Relates the magnetic field B
around a current to the
current Iencl through a surface.
Also Ch. 30: The Magnetic Flux
through a surface is defined as
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Changing Electric Fields Produce Magnetic
Fields: Ampère’s Law & Displacement Current
Maxwell’s Generalization of Ampère’s Law
Ch. 31: Faraday’s Law:
“The emf induced in a
circuit is equal to the time
rate of change of magnetic
flux through the circuit.”
So, changing Magnetic
Fields produce currents
& thus Electric Fields.
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Maxwell’s reasoning about
Ampère’s Law:
In order it to hold, it can’t matter
which surface is chosen. But look
at a discharging capacitor; there is
a current through surface 1 but
none through surface 2:
Therefore, Maxwell modified Ampère’s Law to include the
creation of a magnetic field by a changing electric field.
Analogous to Faraday’s Law which says that electric fields can be
produced by changing magnetic fields. In the case shown, the
electric field between the plates of the capacitor is changing & so:
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Example: Charging capacitor.
A 30-pF air-gap capacitor has circular plates of area A = 100
cm2. It is charged by a 70-V battery through a 2.0-Ω resistor.
At the instant the battery is connected, the electric field
between the plates is changing most rapidly. At this instant,
calculate (a) the current into the plates, and (b) the rate of
change of electric field between the plates. (c) Determine the
magnetic field induced between the plates. Assume E is
uniform between the plates at any instant and is zero at all
points beyond the edges of the plates.
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The second term in Ampere’s Law, first
written by Maxwell, has the dimensions of a
current (after factoring out the μ0), and is
sometimes called the displacement current:
where
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Gauss’s Law for Magnetism
Gauss’s law relates the electric field on a
closed surface to the net charge enclosed by
that surface. The analogous law for magnetic
fields is different, as there are no single
magnetic point charges (monopoles):
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Maxwell’s Equations
We now have a complete set of equations that
describe electric and magnetic fields, called
Maxwell’s Equations. In the absence of dielectric
or magnetic materials, they are:
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Production of Electromagnetic Waves
Since a changing electric field produces a magnetic
field, and a changing magnetic field produces an
electric field, once sinusoidal fields are created,
they can propagate on their own.
These propagating fields are called electromagnetic
waves.
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Oscillating charges will
produce electromagnetic
waves:
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Close to the antenna, the
fields are complicated,
and are called the near
field:
Far from the source, the waves are plane waves:
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The electric and magnetic waves are perpendicular
to each other, and to the direction of propagation.
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