The turning effect of a motor coil

Three motor coils have $40$, $80$ and $160$ turns, each of area $0.004\ \text{m}^2$. Each carries $2\ \text{A}$ in a field of $0.15\ \text{T}$. You will make the program find the largest turning effect of each, the turning effect of the $80$-turn coil at $60^\circ$, and the number of turns that gives $0.3\ \text{N m}$. Then it draws the turning effect against the angle.

The idea. The largest turning effect is $\tau = NBIA$. At an angle $\alpha$ between the plane of the coil and the field, it is $NBIA\cos\alpha$.

Your tasks.

1. Inside the loop, work out t_max, the largest turning effect of the coil with N turns.
2. Find t60, the turning effect of the $80$-turn coil at $60^\circ$.
3. Find N_needed, the number of turns that gives a largest turning effect of $0.3\ \text{N m}$.