Question

A right-circular solenoid of finite length L and radius a has N turns per unit length and carries a current I. Show that the magnetic induction on the cylinder axis

in the limit NLis B_{2}=\frac{\mu_{0} N I}{2}\left(\cos \theta_{1}+\cos \theta_{2}\right) where the angles are defined in the figure.

Fig: 1

Fig: 2

Fig: 3

Fig: 4