Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then ={} B(r) = A(r) = √x2 + y2 is the distance to the z-axis and B is a constant that depends on the current strength I and the spacing of where r = the turns of wire. The vector potential for B is if Bk if I.B. (R²B (-2,3,0) if r> R r
Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then ={} B(r) = A(r) = √x2 + y2 is the distance to the z-axis and B is a constant that depends on the current strength I and the spacing of where r = the turns of wire. The vector potential for B is if Bk if I.B. (R²B (-2,3,0) if r> R r
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then
={}
B(r) =
A(r) =
√x2 + y2 is the distance to the z-axis and B is a constant that depends on the current strength I and the spacing of
where r =
the turns of wire.
The vector potential for B is
if
Bk if
I.B.
(R²B (-2,3,0) if
r> R
r<R
BdS =
R
& A. dr =
(a) Use Stokes' Theorem to compute the flux of B through a circle in the xy-plane of radius r = 6 < R.
(Use symbolic notation and fractions where needed.)
12
if r < R
S
q
(b) Use Stokes' Theorem to compute the circulation of A around the boundary C of a surface lying outside the solenoid.
(Use symbolic notation and fractions where needed.)
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