In Problem 42, a formula for the magnetic field along the axis of a solenoid is given. For x?>> ??and ??> R, the angles ?₁ and ?₂ in Equation 29-35 are very small, so the small-angle approximation cos ? ? 1 ? ?²/2 is valid.

(a) Draw a diagram and show that

(b) Show that the magnetic field at a point far from either end of the solenoid can be written

Where r₁ = x?? ?? is the distance to the near end of the solenoid, r₂ = x?+???is the distance to the far end, and q_m = nIpR2 = ?/ l , where ? = NIpR2 is the magnetic moment of the solenoid.

29-35 B = Honl(cos 0, - cos 0,) R and 02