Electromagnetic Waves Ch' 32

1
Electromagnetic Waves Ch. 32
Maxwells equations (sec. 32.1) Plane EM waves
speed of light (sec. 32.2) The EM
spectrum (sec. 32.6)
C 2007 J. Becker
2
MAXWELLS EQUATIONS
The relationships between electric and magnetic
fields and their sources can be stated compactly
in four equations, called Maxwells equations.
Together they form a complete basis for the
relation of E and B fields to their sources.
C 2004 Pearson Educational / Addison Wesley
3
A capacitor being charged by a current ic has a
displacement current equal to iC between the
plates, with displacement current iD e A dE/dt.
This changing E field can be regarded as the
source of the magnetic field between the plates.
4
A capacitor being charged by a current iC has a
displacement current equal to iC in magnitude
between the plates, with DISPLACEMENT CURRENT
iD e A dE/dt From C e A / d and DV E d
we can use q C V to get q (e A / d ) (E d )
e E A e F E and from iC dq / dt e A
dE / dt e dF E / dt iD We have now seen
that a changing E field can produce a B
fieldand from Faradays Law a changing B field
can produce an E field (or emf)
C 2007 J. Becker
5
MAXWELLS EQUATIONS
The relationships between electric and magnetic
fields and their sources can be stated compactly
in four equations, called Maxwells equations.
Together they form a complete basis for the
relation of E and B fields to their sources.
C 2004 Pearson Educational / Addison Wesley
6
An electromagnetic wave front. The plane
representing the wave front (yellow) moves to the
right with speed c. The E and B fields are
uniform over the region behind the wave front but
are zero everywhere in front of it.
7
Gaussian surface for a plane electromagnetic
wave.
The total electric flux and total magnetic flux
through the surface are both zero.
8
Applying Faradays law to a plane wave.

• ò E dl - d FB /dt
• 1. ò E o dl -Ea (cos 90o 0)
• In time dt the wave front moves to the right a
  distance c dt. The magnetic flux through the
  rectangle in the xy-plane increases by an amount
  d FB equal to the flux through the shaded
  rectangle in the xy-plane with area ac dt, that
  is, d FB Bac dt. So-d FB / dt -Bac and
  E Bc

9
Applying Amperes law to a plane wave.
ò B dl mo eo d FE /dt 1. ò B o dl Ba
(cos 90o 0) 2. In time dt the wave
front moves to the right a distance c dt. The
electric flux through the rectangle in the
xz-plane increases by an amount d FE equal to E
times the area ac dt of the shaded rectangle,
that is, d FE Eac dt. Thus d FE / dt Eac.
Ba mo eo Eac ? B mo eo Ec and from E
Bc and B mo eo EcWe must have c 1 / (mo
eo)1/2 c 3.00 (10)8 m/sec
10
Faradays law applied to a rectangle with height
a and width Dx parallel to the xy-plane.
11
Amperes law applied to a rectangle with height a
and width Dx parallel to the xz-plane.
12
Representation of the electric and magnetic
fields in a propagating wave. One wavelength is
shown at time t 0. Propagation direction is E
x B.
13
Wave front at time dt after it passes through a
stationary plane with area A. The volume between
the plane and the wave front contains an amount
of electromagnetic energy uAc dt.
14
A standing electromagnetic wave does not
propagate along the x-axis instead, at every
point on the x-axis the E and B fields simply
oscillate.
15
Examples of standing electromagnetic waves
Microwave ovens have a standing wave with l
12.2 cm, a wavelength that is strongly absorbed
by water in foods. Because the wave has nodes
(zeros) every 6.1 cm the food must be rotated
with cooking to avoid cold spots!Lasers are
made of cavities of length L with highly
reflecting mirrors at each end to reflect waves
with wavelengths that satisfy L m l / 2, where
m 1, 2, 3,
C 2007 J. Becker
16
The electromagnetic spectrum. The frequencies
and wavelengths found in nature extend over a
wide range. The visible wavelengths extend from
approximately 400 nm (blue) to 700 nm (red).
17
One cycle in the production of an
electro-magnetic wave by an oscillating electric
dipole antenna. The red arrows represent the E
field. (B not shown.)
18
Review
See www.physics.edu/becker/physics51
C 2007 J. Becker