Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Question
Chapter 8.1, Problem 8.2P
(a)
To determine
The electric and magnetic fields in the gap as functions of distance from the axis and time.
(b)
To determine
The energy density and Poynting vector in the gap.
To Verify: the continuity equation.
(c)
To determine
The total energy, the total power flowing into the gap as a function of time
To Check: the power input is equal to the rate of increase of energy within the gap.
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Students have asked these similar questions
Example 7.7. A uniform magnetic field B(1), pointing straight up, fills the
shaded circular region of Fig. 7.25. If B is changing with time, what is the in-
duced electric field?
Solution
E points in the circumferential direction, just like the magnetic field inside a long
straight wire carrying a uniform current density. Draw an Amperian loop of radius
s, and apply Faraday's law:
do
E-d1 = E(27s) =
(s²B(1))
=-7S
2 dB
di
dt
Therefore
s dB
E
2 dr
If B is increasing, E runs clockwise, as viewed from above.
13 Magnetostatics holds only for time-independent currents, but there is no such restriction on 3B/ar.
Chapter 7 Electrodynamics
B(1)
E
Amperian loop
FIGURE 7.25
dt
Rotation
direction
dl
λ
FIGURE 7.26
Problem 9.9 Write down the (real) electric and magnetic fields for a monochro-
matic plane wave of amplitude Eo, frequency w, and phase angle zero that is (a)
traveling in the negative x direction and polarized in the z direction; (b) traveling in
the direction from the origin to the point (1, 1, 1), with polarization parallel to the
xz plane. In each case, sketch the wave, and give the explicit Cartesian components
of k and în.
2.17 A uniform plane wave in free space is normally incident onto a dense
dielectric plate of thickness /4, having refractive index n. Find the required
value of n such that exactly half the incident power is reflected (and half
transmitted). Remember that n > 1.
Chapter 8 Solutions
Introduction to Electrodynamics
Knowledge Booster
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