Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 29.3, Problem 29.4QQ
To determine
The rank of the closed path from a
d
∮ B → ⋅ d s →
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Biot-Savart’ s Law.
2. Line x = O, y = 0, 0 ¡ z ¡ 10 m carries current 2 A along az. Calculate H at points:(a) (5,5,0)(b) (5,15,0)(c) (5,-15,0)
Figure 8 shows a coaxial cable (two nested cylinders) of length l, inner radius a and outer radiusb. Note that l >> a and l >> b. The inner cylinder is charged to +Q and the outer cylinder ischarged to −Q.The cable carries a current I, which flows clockwise. Use Ampere’s Law to calculate themagnetic field B⃗ at r < a, a < r < b, and r > b.
2. The current distribution of an infinite,
wire can be described in cylindrical coordinates by
J = J(p) 2.
longitudinally-uniform, and axially-symmetric
(a) Show that. J = 0.
(b) Considerations of longitudinal and axial symmetry require that the mag-
netic field can only depend upon p, i.e. that
B(p) = Bp(p)ô + Bø(p) + B₂(p)2.
Use Ampère's Law to determine B6 (p) in terms of I (p) = 2π J(p') p'dp'.
(c) Use the Biot and Savart Law to show that Bp(p) = B₂ (p) = 0. Side note:
it is pretty easy to show that B,(p) must be zero using Gauss's Law for
B with a cylindrical volume. I am not aware of an "easy" way to see
B₂ (p) = 0 - not that it is very difficult using the Biot and Savart Law...
(d) Use the integral form for the vector potential [Jackson, Eq. (5.32)] to
determine A for this current distribution. Hint: in order to deal with
divergent integrals, you may want to limit the current distribution to
-L ≤ z ≤ L, determine A, adjust A by a constant (as one is allowed to
do), and then…
Chapter 29 Solutions
Physics for Scientists and Engineers
Ch. 29.1 - Consider the magnetic field due to the current in...Ch. 29.2 - A loose spiral spring carrying no current is hung...Ch. 29.3 - Prob. 29.3QQCh. 29.3 - Prob. 29.4QQCh. 29.4 - Consider a solenoid that is very long compared...Ch. 29 - Calculate the magnitude of the magnetic field at a...Ch. 29 - You are working as an expert witness in a civil...Ch. 29 - In Niels Bohrs 1913 model of the hydrogen atom, an...Ch. 29 - Prob. 4PCh. 29 - Prob. 5P
Ch. 29 - Consider a flat, circular current loop of radius R...Ch. 29 - Prob. 7PCh. 29 - One long wire carries current 30.0 A to the left...Ch. 29 - Determine the magnetic field (in terms of I, a,...Ch. 29 - Prob. 10PCh. 29 - Two long, parallel wires carry currents of I1 =...Ch. 29 - Prob. 12PCh. 29 - Prob. 13PCh. 29 - Prob. 14PCh. 29 - You are part of a team working in a machine parts...Ch. 29 - Why is the following situation impossible? Two...Ch. 29 - Prob. 17PCh. 29 - Niobium metal becomes a superconductor when cooled...Ch. 29 - The magnetic coils of a tokamak fusion reactor are...Ch. 29 - A packed bundle of 100 long, straight, insulated...Ch. 29 - The magnetic field 40.0 cm away from a long,...Ch. 29 - Prob. 22PCh. 29 - A long solenoid that has 1 000 turns uniformly...Ch. 29 - A certain superconducting magnet in the form of a...Ch. 29 - Prob. 25PCh. 29 - You are given a certain volume of copper from...Ch. 29 - Prob. 27PCh. 29 - You are working for a company that creates special...Ch. 29 - A solenoid of radius r = 1.25 cm and length =...Ch. 29 - The magnetic moment of the Earth is approximately...Ch. 29 - A 30.0-turn solenoid of length 6.00 cm produces a...Ch. 29 - Why is the following situation impossible? The...Ch. 29 - Suppose you install a compass on the center of a...Ch. 29 - Prob. 34APCh. 29 - A nonconducting ring of radius 10.0 cm is...Ch. 29 - Prob. 36APCh. 29 - A very large parallel-plate capacitor has uniform...Ch. 29 - Two circular coils of radius R, each with N turns,...Ch. 29 - Prob. 39APCh. 29 - Two circular loops are parallel, coaxial, and...Ch. 29 - As seen in previous chapters, any object with...Ch. 29 - Review. Rail guns have been suggested for...Ch. 29 - Prob. 43APCh. 29 - An infinitely long, straight wire carrying a...Ch. 29 - Prob. 45CPCh. 29 - We have seen that a long solenoid produces a...Ch. 29 - A wire carrying a current I is bent into the shape...Ch. 29 - Prob. 48CPCh. 29 - Prob. 49CPCh. 29 - Prob. 50CPCh. 29 - The magnitude of the force on a magnetic dipole ...
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