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Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then 0 Bk B(r) = if r> R if 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) = R²B (3.0) if B(-y, x,0) (18²8) r> R if r < R

Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then 0 Bk B(r) = if r> R if 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) = R²B (3.0) if B(-y, x,0) (18²8) r> R if 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 S 0 Incorrect Bk if Jc if r> R r<R (R²B (-2,0) if if r> R B(-y, x,0) if <R (a) Use Stokes' Theorem to compute the flux of B through a circle in the xy-plane of radius = 6 < R. (Use symbolic notation and fractions where needed.) B.dS= R A dr = 2 Вп п (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.) S 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) = 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 S 0 Incorrect Bk if Jc if r> R r<R (R²B (-2,0) if if r> R B(-y, x,0) if <R (a) Use Stokes' Theorem to compute the flux of B through a circle in the xy-plane of radius = 6 < R. (Use symbolic notation and fractions where needed.) B.dS= R A dr = 2 Вп п (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.) S 0
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