Chapter 30
Maxwell’s Equations and Electromagnetic Waves
Conceptual Problems
1
•
[SSM]
True or false:
(
a
) The displacement current has different units than the conduction current.
(
b
) Displacement current only exists if the electric field in the region is changing
with time.
(
c
) In an oscillating
LC
circuit, no displacement current exists between the
capacitor plates when the capacitor is momentarily fully charged.
(
d
) In an oscillating
LC
circuit, no displacement current exists between the
capacitor plates when the capacitor is momentarily uncharged.
(
a
) False. Like those of conduction current, the units of displacement current are
C/s.
(
b
) True. Because displacement current is given by
dt
d
I
e
0
d
φ
∈
=
,
I
d
is zero if
0
e
=
dt
d
.
(
c
) True. When the capacitor is fully charged, the electric flux is momentarily a
maximum (its rate of change is zero) and, consequently, the displacement current
between the plates of the capacitor is zero.
(
d
) False.
I
d
is zero if
0
e
=
dt
d
. At the moment when the capacitor is
momentarily uncharged,
dE
/
dt
≠
0 and so
0
e
≠
dt
d
.
2
•
Using SI units, show that
dt
d
I
e
0
d
=
has units of current.
Determine the Concept
We need to show that
dt
d
e
0
has units of amperes.
We can accomplish this by substituting the SI units of
0
and
dt
d
e
and
simplifying the resulting expression.
A
s
C
V
V
s
C
s
V
C
N
C
s
V
N
C
s
m
m
V
m
N
C
2
2
2
=
=
⋅
=
⋅
=
⋅
=
⋅
⋅
⋅
3
•
[SSM]
True or false:
(
a
)
Maxwell’s equations apply only to electric and magnetic fields that are
constant over time.
2829
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(
b
)
The electromagnetic wave equation can be derived from Maxwell’s
equations.
(
c
)
Electromagnetic waves are transverse waves.
(
d
)
The electric and magnetic fields of an electromagnetic wave in free space
are in phase.
(
a
) False. Maxwell’s equations apply to both timeindependent and time
dependent fields.
(
b
) True. One can use Faraday’s law and the modified version of Ampere’s law to
derive the wave equation.
(
c
) True. Both the electric and magnetic fields of an electromagnetic wave
oscillate at right angles to the direction of propagation of the wave.
(
d
) True.
4
•
Theorists have speculated about the existence of
magnetic monopoles
,
and several experimental searches for such monopoles have occurred. Suppose
magnetic monopoles were found and that the magnetic field at a distance
r
from a
monopole of strength
q
m
is given by
B
= (
μ
0
/4
π
)
q
m
/
r
2
. Modify the Gauss’s law for
magnetism equation to be consistent with such a discovery.
Determine the Concept
Gauss’s law for magnetism would become
inside
m,
0
S
n
q
dA
B
=
∫
where
q
m, inside
is the total magnetic charge inside the
Gaussian surface. Note that Gauss’s law for electricity follows from the existence
of electric monopoles (charges), and the electric field due to a point charge
follows from the inversesquare nature of Coulomb’s law.
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 Summer '08
 Wei
 Current

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