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

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Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then
(0 if r> R
B(r) =
Bk if r< R
where r= V
+ 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
RB (-.0) if
B(-y. x,0)
r> R
A(r) =
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
Incorrect
(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.)
A - dr =
Transcribed Image Text:Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then (0 if r> R B(r) = Bk if r< R where r= V + 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 RB (-.0) if B(-y. x,0) r> R A(r) = 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 Incorrect (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.) A - dr =
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