This homework assignment is due Thursday, 9 April in time for Lab #8.

Consider a solenoid with N turns, height h, radius 1 and a current 4π/μ_o flowing through it. The central axis of the coils is along the z-axis. The solenoid begins at (1,0,h/2) and spirals down to (1,0,-h/2), thus the current flows downward in the z-direction.

In class we showed that the Biot-Savart law may be approximated by

   ΔB ≈ Δs × r_vec / r³.

For a current loop centered in the x-y plane with the current at (1,0,0) flowing in the y-direction, we found that

   Δs = aΔθ (-sin θ , cos θ)

and

   r_vec = (x - cos θ , y - sin θ, z).

Modify each of these for the solenoid described, above.

    
% r-vector parameters
    r = [
        x - cos(th)
        y - sin(th)
        z - h/2*(1 - th/N/pi)
        ];

% delta s
    ds = [
        dTh * [
        -sin(th)
        cos(th)
        ]
        ds_z
        ];