Essential University Physics
4th Edition
ISBN: 9780134988566
Author: Wolfson, Richard
Publisher: Pearson Education,
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Textbook Question
Chapter 26, Problem 86P
Derive Equation 26.20 by considering the current sheet to be made of infinitely many infinitesimal line currents.
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Students have asked these similar questions
Two straight, parallel, superconducting wires 4.5 mm apart carry equal currents of 15,000 A in opposite directions. What force, per unit length, does each wire exert on the other?
A scientist wants to study the in-plane spiral tubes used in chemical reactors. To
proceed with his study, he took a thin insulated wire and converted it into a plane
spiral of 140 closely wounded turns. The required field at the centre of the spiral is
8.8 µT and the current flowing across the spiral is 10 mA. In the given figure, the
radius of the inner turns is a and the radius of the outer turns is b. If b is twice of a
then find the inner and outer radii to conduct the experiment.
(Use In (2) = 0.693)
Q.
O 75 mm, 150 mm
55.4 mm, 110.8 mm
80 mm, 160 mm
69.3 mm, 138.6 mm
a
As a numerical example illustrating the use of (9), we determine H at P₂(0.4, 0.3, 0)
in the field of an 8. A filamentary current is directed inward from infinity to the origin
on the positive x axis, and then outward to infinity along the y axis. This arrangement
is shown in Figure 7.6.
Solution. We first consider the semi-infinite current on the x axis, identifying the
two angles, α1x = -90° and a2x = tan-¹ (0.4/0.3) = 53.1°. The radial distance
P
is
measured from the x axis, and we have px = 0.3. Thus, this contribution to H₂ is
2
12
8
(1.8)ap
-ap
H₂(x)
-(sin 53.1° + 1)a
0.3л
J
4л (0.3)
The unit vector a must also be referred to the x axis. We see that it becomes -az.
Therefore,
12
H2(x)
=-=a₂ A/m
J
For the current on the y axis, we have any = -tan-¹(0.3/0.4) = -36.9°, a2y = 90°,
and py= 0.4. It follows that
8
H₂(y)
8
4л (0.4)
(1 + sin 36.9°)(-a₂) = -a- A/m
J
8 A
8 A
How were the
angles
calculated,
please explain.
α2x
P₂(0.4, 0.3, 0)
α1x
Figure 7.6 The individual fields of two…
Chapter 26 Solutions
Essential University Physics
Ch. 26.2 - The figure shows a proton in a magnetic field. (1)...Ch. 26.3 - A proton of the same energy as the electron in...Ch. 26.4 - Prob. 26.4GICh. 26.5 - Prob. 26.5GICh. 26.6 - Prob. 26.6GICh. 26.7 - Which of the following best describes the...Ch. 26.8 - The figure shows three parallel wires carrying...Ch. 26 - An electron moving with velocity v through a...Ch. 26 - A magnetic field points out of this page. Will a...Ch. 26 - Do particles in a cyclotron gain energy from the...
Ch. 26 - Two identical particles carrying equal charge are...Ch. 26 - Prob. 5FTDCh. 26 - Do currents in the same direction attract or...Ch. 26 - If a current is passed through an unstretched...Ch. 26 - Figure 26.38 shows some magnetic field lines...Ch. 26 - Prob. 9FTDCh. 26 - Prob. 10FTDCh. 26 - Find (a) the minimum magnetic field needed to...Ch. 26 - An electron moving at right angles to a 0.10-T...Ch. 26 - Find the magnitude of the magnetic force on a...Ch. 26 - The magnitude of Earths magnetic field is about...Ch. 26 - A velocity selector uses a 60-mT magnetic field...Ch. 26 - Prob. 16ECh. 26 - How long: does it take an electron to complete a...Ch. 26 - Radio astronomers detect electromagnetic radiation...Ch. 26 - Prob. 19ECh. 26 - Two protons, moving in a plane perpendicular to a...Ch. 26 - Find the magnitude of the force on a 65.5-cm-long...Ch. 26 - A wire carrying 15 A makes a 25 angle with a...Ch. 26 - In an experimental nuclear fusion reactor, plans...Ch. 26 - A wire with mass per unit length 75 g/m runs...Ch. 26 - A wire carries 6.71 A. You form it into a...Ch. 26 - A single-turn wire loop is 2.0 cm in diameter and...Ch. 26 - A 2.2-m-long wire carrying 3.5 A is wound into a...Ch. 26 - Whats the current in a long wire if the magnetic...Ch. 26 - In standard household wiring, parallel wires about...Ch. 26 - Earths magnetic dipole moment is 8.01022 Am2. Find...Ch. 26 - A single-turn square wire loop 18.0 cm on a side...Ch. 26 - An electric motor contains a 250-turn circular...Ch. 26 - The line integral of the magnetic field on a...Ch. 26 - The magnetic field shown in Fig. 26.39 has uniform...Ch. 26 - Number 12 gauge wire, commonly used in household...Ch. 26 - Prob. 36ECh. 26 - A superconducting solenoid has 3300 turns per...Ch. 26 - Example 26.2: Chlorine is an unusual element in...Ch. 26 - Example 26.2: You’re trying to measure arsenic...Ch. 26 - Example 26.2: A beam of elections is initially...Ch. 26 - Example26.2: The mass spectrometer described in...Ch. 26 - Example 26.7: A long, straight wire 9.27 mm in...Ch. 26 - Example 26.7: Niobium-tin, a commonly used...Ch. 26 - Prob. 44ECh. 26 - Example 26.7: A coaxial cable like the one...Ch. 26 - Prob. 46PCh. 26 - Jupiter has the strongest magnetic field in our...Ch. 26 - A proton moving with velocity v1 = 3.6 104 m/s...Ch. 26 - A simplified model of Earths magnetic field has it...Ch. 26 - Before the advent of today’s flat-screen...Ch. 26 - Show that the orbital radius of a charged particle...Ch. 26 - Prob. 52PCh. 26 - Prob. 53PCh. 26 - Prob. 54PCh. 26 - Youre designing a prosthetic ankle that includes a...Ch. 26 - A 20-cm-long conducting rod with mass 18 g is...Ch. 26 - Prob. 57PCh. 26 - Nuclear magnetic resonance (NMR) is a technique...Ch. 26 - A wire carrying 1.5 A passes through a 48-mT...Ch. 26 - Your smartphone contains a magnetometer that uses...Ch. 26 - A single piece of wire carrying current I is bent...Ch. 26 - You and a friend get lost while hiking, so your...Ch. 26 - Part of a long wire carrying current I is bent...Ch. 26 - A long, straight wire carries a 25-A current. A...Ch. 26 - A long conducting rod of radius R carries a...Ch. 26 - A long, hollow conducting pipe of radius R carries...Ch. 26 - You have 10 m of 0.50-mm-diameter copper wire and...Ch. 26 - Prob. 69PCh. 26 - The largest lightning strikes have peak currents...Ch. 26 - Prob. 71PCh. 26 - Prob. 72PCh. 26 - Prob. 73PCh. 26 - A circular wire loop of radius 15 cm and...Ch. 26 - Prob. 75PCh. 26 - A long, hollow conducting pipe of radius R and...Ch. 26 - A solid conducting wire of radius R runs parallel...Ch. 26 - A disk of radius a carries uniform surface charge...Ch. 26 - Youre developing a system to orient an orbiting...Ch. 26 - Prob. 80PCh. 26 - Prob. 81PCh. 26 - Find an expression for the magnetic field at the...Ch. 26 - Prob. 83PCh. 26 - A Helmholtz coil is a pair of identical circular...Ch. 26 - Prob. 85PCh. 26 - Derive Equation 26.20 by considering the current...Ch. 26 - Your roommate is sold on magnet therapy, a sham...Ch. 26 - A toroid is a solenoid-like coil bent into a...Ch. 26 - A toroid is a solenoid-like coil bent into a...Ch. 26 - A toroid is a solenoid-like coil bent into a...Ch. 26 - A toroid is a solenoid-like coil bent into a...
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