Answered: Let A be the vector potential and B the…

Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then fo if r>R | Bk if rR AG) = if r

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter31: Gauss’s Law For Magnetism And Ampère’s Law

Section: Chapter Questions

Problem 28PQ: Sketch a plot of the magnitude of the magnetic field as a function of position r for a coax (Fig....

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Question

17.2 - #9

Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then
So if r>R
Bk if r<R
B(r) =
where r= Vx + y is the distance to the z-axis and B is a constant that depends on the current strength I and the
spacing of the turns of wire.
The vector potential for B is
S ŹR°B(-.0) if
r> R
A(r) =
B(-y.x,0)
if
r<R
(a) Use Stokes' Theorem to compute the flux of B through a circle in the xy-plane of radius r = 2 < R.
(Use symbolic notation and fractions where needed.)
B- dS =
(b) Use Stokes' Theorem to compute the circulation of A around the boundary Cof a surface lying outside the solenoid.
(Use symbolic notation and fractions where needed.)
dr =

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