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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) = 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
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) = 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.)
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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