Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
A solid sphere with radius R and charge density p(r) = kr is centered at the origin and spinning with an angular velocity, w, about the z-axis (@= @ 2). a) Using the results of example 5.11, find the magnetic vector potential, A, inside the spinning charged sphere. Express your answer in terms of the total charge, Q, of the sphere. b) What is the magnetic field (magnitude and direction) at the center of this spinning sphere? c) Determine the magnetic field, B, outside the spinning sphere. d) Using the results of part c), find the magnetic dipole moment, m, of this spinning sphere.

A solid sphere with radius R and charge density p(r) = kr is centered at the origin and spinning with an angular velocity, w, about the z-axis (@= @ 2). a) Using the results of example 5.11, find the magnetic vector potential, A, inside the spinning charged sphere. Express your answer in terms of the total charge, Q, of the sphere. b) What is the magnetic field (magnitude and direction) at the center of this spinning sphere? c) Determine the magnetic field, B, outside the spinning sphere. d) Using the results of part c), find the magnetic dipole moment, m, of this spinning sphere.

icon
Related questions
Question

The results of 5.11 are added, need help setting up and solving.

A solid sphere with radius R and charge density p(r) = kr is centered at the origin and spinning with an angular velocity, w, about the z- - axis (@= @ 2). a) Using the results of example 5.11, find the magnetic vector potential, A, inside the spinning charged sphere. Express your answer in terms of the total charge, Q, of the sphere. b) What is the magnetic field (magnitude and direction) at the center of this spinning sphere? c) Determine the magnetic field, B, outside the spinning sphere. d) Using the results of part c), find the magnetic dipole moment, m, of this spinning sphere.
Transcribed Image Text:A solid sphere with radius R and charge density p(r) = kr is centered at the origin and spinning with an angular velocity, w, about the z- - axis (@= @ 2). a) Using the results of example 5.11, find the magnetic vector potential, A, inside the spinning charged sphere. Express your answer in terms of the total charge, Q, of the sphere. b) What is the magnetic field (magnitude and direction) at the center of this spinning sphere? c) Determine the magnetic field, B, outside the spinning sphere. d) Using the results of part c), find the magnetic dipole moment, m, of this spinning sphere.
for points inside the sphere, Ho Ro 3 MORAO (@xr), for points outside the sphere. 3r3 Having evaluated the integral, I revert to the "natural" coordinates of Fig. 5.45, in which w coincides with the z axis and the point r is at (r, 0, 0): (r< R), A(r) = (@x r), A(r, 0,0) = Ho Rwo r sine, 3 MoR¹ wo sine 3 p2 $, (r≥ R). (5.68) (5.69)
Transcribed Image Text:for points inside the sphere, Ho Ro 3 MORAO (@xr), for points outside the sphere. 3r3 Having evaluated the integral, I revert to the "natural" coordinates of Fig. 5.45, in which w coincides with the z axis and the point r is at (r, 0, 0): (r< R), A(r) = (@x r), A(r, 0,0) = Ho Rwo r sine, 3 MoR¹ wo sine 3 p2 $, (r≥ R). (5.68) (5.69)
Expert Solution
steps

Step by step

Solved in 6 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer