CHAPTER
24
ELECTROMAGNETIC WAVES
ANSWERS TO FOCUS ON CONCEPTS QUESTIONS
1.
(b)
The loop can only detect the wave if the wave’s magnetic field has a component
perpendicular to the plane of the loop, that is, along the
y
axis.
Only then will there be a
changing magnetic flux through the loop.
The changing flux is needed, so that an induced
emf will arise in the loop according to Faraday’s law of electromagnetic induction.
The
electric and magnetic fields of an electromagnetic wave are mutually perpendicular and are
both perpendicular to the direction in which the wave travels.
Thus, when the wave travels
along the
z
axis with its electric field along the
x
axis, the magnetic field will be along the
y
axis as needed.
2.
(c)
The wavelength
λ
, frequency
f
, and speed
c
of an electromagnetic wave are related
according to
c
=
f
λ
, where
c
is the same for any electromagnetic wave traveling in a vacuum
and is independent of
λ
and
f
.
Since
c
is constant,
λ
and
f
are inversely proportional.
When
f
is reduced by a factor of three,
λ
increases by a factor of three.
3.
(b)
The magnitudes of the electric and magnetic fields of the wave are proportional to each
other, according to
E
=
cB
(Equation 24.3).
As Section 24.4 discusses, the wave carries
equal amounts of electric and magnetic energy.
4.
(a)
The magnitudes of the electric and magnetic fields of the wave are proportional,
according to
E
=
cB
(Equation 24.3).
Thus, when
E
doubles, so does
B
.
The total energy
density
and the intensity are each proportional to the square of the electric field magnitude,
according to
2
0
u
E
ε
=
(Equation 24.2b) and
2
0
S
c E
=
(Equation 24.5b),
Therefore, when
E
doubles,
u
and
S
both increase by a factor of 2
2
= 4.
5.
698 J/(s·m
2
)
6.
(d)
The observed frequency is
rel
o
s
1
v
f
f
c
=
±
according to Equation 24.6.
The frequency
f
s
emitted by the source is the same in each case, so that only the relative speed
v
rel
and the
direction of the relative motion determine the observed frequency.
In each case either the
source or the observer is moving, so the relative speed is just the magnitude of the velocity
vector shown in the drawing.
Since the velocity vector has the same magnitude in each case,
the relative speed is the same in each case.
Thus, it is only the direction of the relative
motion that needs to be considered here.
In A and C the source and observer are moving
apart at the same relative speed, the minus sign applies in Equation 24.6, and the observed
frequencies are the same.
In B and D they are coming together at the same relative speed, the