In this problem, use Ampere'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 Ampere'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.

Transcribed Image Text:

10 b -Rectangular path