An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Question
Chapter 8.2, Problem 22P
To determine
The analogue of equation
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Consider a spring made of a superconducting material (electrical resistance very close to zero) containing N turns, radius R, natural length X0 and elastic constant k, as shown in the figure opposite. Somehow, an electric current I0 is passed through the spring. Calculate the spring length variation at the new equilibrium state. Tip: the magnetic flux over the spring must be constant at all times.
For Problem 8.16, how do I prove the relations and give the correct expressions?
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
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