Answer Happy

5. An infinitely long solenoid has n turns per unit length, radius R, and carries current 1. As we sand zero lessons, the magnetic field B for an infinitely long solenoid is B = outside the solenoid. Honl2 inside the solenoid and zero (a) [10 points] Show that the magnetic vector potential A of the infinitely long solenoid is ifs < R A = Honls 2 Honl R2 ifs > R 2 S [Hint: Since the current density J(r') in the solenoid goes to infinity, you cannot find A with Ho (J(r') dr'. ↑ However, you can use the result we derived in class that the circulation of A is given by f^ di = ff, vx V x A da = SS₁ B-da = . ] (b) Show that the vector potential A in (a) does indeed give the correct expression for the magnetic field B both inside the solenoid and outside the solenoid, as noted in the statement of the problem. [10 points] A dl