In this problem, use Ampre's law to show that the magnetic field inside a long solenoid is B = 0nI. Assume that the field inside

In this problem, use Ampère's law to show that the magnetic field inside a long solenoid is B = μ0nI. Assume that the field inside the solenoid is uniform and parallel to the axis and that the field outside is zero. Choose a rectangular path for Ampère's law.

(a) Write down B||Δl for each of the four sides of the path, in terms of B, a, (the short side) and b (the long side).
(b) Sum these to form the circulation.
(c) Now, to find the current cutting through the path: each loop carries the same current I, and some number N of loops cut through the path, so the total current is NI. Rewrite N in terms of the number of turns per unit length (n) and the physical dimensions of the path.
(d) Solve for B.

Rectangular path