Homework Help is Here – Start Your Trial Now!
Science
Physics
Problem 1: Field angular momentum A pure magnetic dipole of dipole moment ñ is placed R + at the center of a spherical shell of radius R carry- ing total charge Q uniformly distributed across its + †ñ + + + + + surface. The dipole and the spherical shell are both initially at rest. (a) Compute the total linear momentum (density j = €0Ë × B) and angular momentum (density l = i x g) stored in the electromagnetic fields in terms of m, Q, and R. (b) The magnetic dipole moment m is slowly changed. Derive the induced electric field Ena (7) = - 40 m x A (1) (HINT: One elegant solution makes use of the dipole vector potential Ãalip (F) = ) (c) Compute the torque on the charged sphere in terms of m, Q, and R. If the dipole moment is turned off completely, how much angular momentum is the sphere left with? (Assume the sphere is heavy enough that its rotation generates negligible magnetic field.) (d) Instead, the magnetic dipole moment m is held fixed and the charged sphere is allowed to gradually expand (driven by electrostatic pressure). Will it begin to rotate? If so, where does the torque come from? +

Problem 1: Field angular momentum A pure magnetic dipole of dipole moment ñ is placed R + at the center of a spherical shell of radius R carry- ing total charge Q uniformly distributed across its + †ñ + + + + + surface. The dipole and the spherical shell are both initially at rest. (a) Compute the total linear momentum (density j = €0Ë × B) and angular momentum (density l = i x g) stored in the electromagnetic fields in terms of m, Q, and R. (b) The magnetic dipole moment m is slowly changed. Derive the induced electric field Ena (7) = - 40 m x A (1) (HINT: One elegant solution makes use of the dipole vector potential Ãalip (F) = ) (c) Compute the torque on the charged sphere in terms of m, Q, and R. If the dipole moment is turned off completely, how much angular momentum is the sphere left with? (Assume the sphere is heavy enough that its rotation generates negligible magnetic field.) (d) Instead, the magnetic dipole moment m is held fixed and the charged sphere is allowed to gradually expand (driven by electrostatic pressure). Will it begin to rotate? If so, where does the torque come from? +

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
See similar textbooks
icon
Related questions
Question

Please use words as well as equations to explain.

Problem 1: Field angular momentum A pure magnetic dipole of dipole moment ñ is placed + + + R at the center of a spherical shell of radius R carry- ing total charge Q uniformly distributed across its + tm £ surface. The dipole and the spherical shell are both initially at rest. + + (a) Compute the total linear momentum (density g = E0Ē x B) and angular momentum (density l = i x g) stored in the electromagnetic fields in terms of m, Q, and R. (b) The magnetic dipole moment ñ is slowly changed. Derive the induced electric field Ena(7) = - 4o m x f 4 r2 (1) (HINT: One elegant solution makes use of the dipole vector potential Ādip(7) = .) (c) Compute the torque on the charged sphere in terms of m, Q, and R. If the dipole moment is turned off completely, how much angular momentum is the sphere left with? (Assume the sphere is heavy enough that its rotation generates negligible magnetic field.) (d) Instead, the magnetic dipole moment ñ is held fixed and the charged sphere is allowed to gradually expand (driven by electrostatic pressure). Will it begin to rotate? If so, where does the torque come from?
Transcribed Image Text:Problem 1: Field angular momentum A pure magnetic dipole of dipole moment ñ is placed + + + R at the center of a spherical shell of radius R carry- ing total charge Q uniformly distributed across its + tm £ surface. The dipole and the spherical shell are both initially at rest. + + (a) Compute the total linear momentum (density g = E0Ē x B) and angular momentum (density l = i x g) stored in the electromagnetic fields in terms of m, Q, and R. (b) The magnetic dipole moment ñ is slowly changed. Derive the induced electric field Ena(7) = - 4o m x f 4 r2 (1) (HINT: One elegant solution makes use of the dipole vector potential Ādip(7) = .) (c) Compute the torque on the charged sphere in terms of m, Q, and R. If the dipole moment is turned off completely, how much angular momentum is the sphere left with? (Assume the sphere is heavy enough that its rotation generates negligible magnetic field.) (d) Instead, the magnetic dipole moment ñ is held fixed and the charged sphere is allowed to gradually expand (driven by electrostatic pressure). Will it begin to rotate? If so, where does the torque come from?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Unit conversion
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS