Lesson 26 - E&M waves II
I.
Basic Properties of E&M Waves
1.
As discussed in the previous lesson, E&M waves are transverse waves. Thus, the
electric and magnetic field vectors must be perpendicular to the direction of
wave propagation.
2.
Maxwell's equations also show that the electric and magnetic field vectors must
be perpendicular to each other.
3.
 

The directions of the three vectors E , B , and v are connected by the
_________________ __________________ ______________________.
EXAMPLE: The three vectors at a single instant of time
v
EXAMPLE: The evolution of the three vectors over time
y
z
x
4.
Maxwell's equations show that the electric and magnetic fields are coupled. The
following three important relationships between the electric and magnetic fields
follow from the solution of Maxwell's equations:
a) The electric and magnetic fields are _____________ _______________
b) The electric and magnetic fields have the ______________ ______________
c) The magnitudes of the electric and magnetic fields at any instant in time are
related by the equation:
E/B=
EXAMPLE: What is the magnetic field strength if the electric field strength of an E&M
wave is 3x10+3 N/C?
5.
The Source of Electromagnetic Waves is ________________________
___________________. This creates a _________________ ________________
____________________ which then creates a ________________________
_____________________ _____________________.
II.
Poynting Vector And Intensity
A.
Electromagnetic waves transfer both energy and linear momentum. In order to
describe the transfer of energy by an E&M wave, we define a special vector
called the Poynting vector that is defined by the equation:

 
1
S  μ E B
o
B.
The direction of the Poynting vector is the ________________ as the
____________________ of ____________________________.
C.
The magnitude of the Poynting vector gives the ______________________ per
unit ________________________ delivered by the _______________________
___________________________.
D.
The magnitude of the Poynting vector changes with time as the electric and
magnetic field vectors change with time. Since most electromagnetic waves vary
quickly with time (a 0.5 m light wave has a frequency of 6.0x1014 Hz), we
usually talk about the average of the magnitude of the Poynting vector.
SAV 
SAV 
SAV  E max Bmax  I
2 μo
The average of the magnitude of the Poynting vector is more commonly called
the intensity of the electromagnetic wave or the "brightness" when talking about
light.
E.
With a little bit of algebra, we can show that the intensity of an electromagnetic
wave is proportional to the ________________ of the ______________________
of the __________________________.
PROOF:
EXAMPLE: What is the maximum power delivered if the amplitude of the electric field
is 1.0x10+3 N/C? (Remember that μ o  4 π x 10 7 Tm/A )
III.
Linear Momentum and Electromagnetic Waves
An electromagnetic wave carries linear momentum. The magnitude of the linear
momentum of a wave of energy E is given by
p=
We can prove that electromagnetic waves have linear momentum by letting the
light shine on an absorber and then measure the force exerted on the absorber.
Electromagnetic
Wave
Absorber
The force applied by the electromagnetic wave upon the absorber according to
Newton's 2nd Law is
By definition, the force divided by area is pressure. Thus, we see that an
electromagnetic wave can supply a "radiation pressure" upon the absorber that is
given by
Another important special case is when an electromagnetic wave is totally reflect
off a material (perfect mirror) as shown below.
Incoming Electromagnetic
Wave
Reflected Electromagnetic
Wave
Mirror
Again the change in the linear momentum of the electromagnetic wave is the
negative of the change of the linear momentum of the mirror.
p =
Following the same process as for the previous case we have
Prad = 2 I / c
IV.
Wave Rronts and Rays
Since a wave has no specific location like a baseball, we can't describe its motion
using a position vector. Thus, we need some other way of describing the motion
of the wave. A convenient way of describing the motion of a wave is to chose to a
particular point on the wave (for example the peak of the wave) and describe its
motion.
A.
A wave front is the geometrical surface corresponding to a constant phase of
the wave.
EXAMPLE: A Plane Wave
E = Emax Cos(kx-t)
y
x
z
B.
Instead of describing the wave by wave fronts, we can sometimes simply replace
a wave front by a single vector arrow that is perpendicular to the wave front
and points in the direction of wave propagation. This vector arrow is called a
Ray.
EXAMPLE: Outgoing Spherical Wave
EXAMPLE: Plane Wave Traveling in +x-Direction
V.
Wave Diffraction
One of the most intriguing properties of a wave is the ability of a wave to bend
around an obstacle (diffraction).
EXAMPLE: You can hear a person calling you from the next room even though you
can't see them. How is this possible?
SOLN:
So why can't you see the person?