In this problem, you will derive Equation 29-37 by another method. Consider a long, tightly wound solenoid of length l and radius R << l lying along the axis with its center at the origin. It has N turns and carries a current I. Consider an element of the solenoid of length dx.

(a) What is the magnetic moment of this element?

(b) Show that the magnetic field dB due to this element at a point on the x axis x₀ far from the element is given by

Where A = πR² and x’ = x₀ – x is the distance from the element to the field point.

(c) Integrate this expression from x = –½ℓ to x = +½ℓ to obtain Equation 29-37.

dx -nIA- d