Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then fo if r>R | Bk if rR AG) = if r

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Chapter1: Units, Trigonometry. And Vectors
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Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then
So if r>R
Bk if r<R
B(r) =
where r= Vx + 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
S ŹR°B(-.0) if
r> R
A(r) =
B(-y.x,0)
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 =
(b) Use Stokes' Theorem to compute the circulation of A around the boundary Cof a surface lying outside the solenoid.
(Use symbolic notation and fractions where needed.)
dr =
Transcribed Image Text:Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then So if r>R Bk if r<R B(r) = where r= Vx + 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 S ŹR°B(-.0) if r> R A(r) = B(-y.x,0) 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 = (b) Use Stokes' Theorem to compute the circulation of A around the boundary Cof a surface lying outside the solenoid. (Use symbolic notation and fractions where needed.) dr =
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