Question

1. An infinite solenoid has n turns per unit length, a radius R, and carries a current I. The magnitude of the magnetic field inside the solenoid is given by B = Mon, pints along the solenoid, and vanishes outside. (a) Find the magnitude of the vector potential, A, at a radius r inside the solenoid. (b) Find the magnitude of the vector potential, A, at a radius r outside the solenoid. Check that your answers agree on the boundary, when r = R. Hint: you can use Stoke's theorem to rewrite the line integral of the vector potential in terms of the magnetic field.

Answer 1

D Consider an infinite solenoid with in turns Per unit longth, radius R and Consying earnt I. The magnetic field insiche is along the axis (2) of the solenoid is givenly Es Nom IZ Now, considerring a corentar Amperican Loop of rading & (ra) inside the solenoid in my plane, we can write & u. dr a foxt. d5 = S. 3. as Le A ar contre ) 2 For a ( - A pont ro for ver cirenless Amperian loop of rading 2) outside the solenoid, 3. di - pont. R² - padra SB. A5 A reo - Pont. HRt À - von IR ô 28 2 put, pak, then. Ā bons Rza R o just from W vector & C We can say the pokental has et rar the same values.