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Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then

Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then

Advanced Engineering Mathematics
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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Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then B(r) = {Bk if <R 0 r> R r where 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 the turns of wire. The vector potential for B is A(r) = { }B (-3,2,0) B(-y.x,0) 8 (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.) B.dS= S Incorrect R²B(-20) if r> R if r < R A dr = (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.) C 2 Br 0
Transcribed Image Text:Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then B(r) = {Bk if <R 0 r> R r where 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 the turns of wire. The vector potential for B is A(r) = { }B (-3,2,0) B(-y.x,0) 8 (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.) B.dS= S Incorrect R²B(-20) if r> R if r < R A dr = (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.) C 2 Br 0
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