Two coils that are separated by a distance equal to their radius and that carry equal currents such that their axial fields add are called Helmholtz coils. A feature of Helmholtz coils is that the resultant magnetic field between the coils is very uniform. Let R = 10 cm, I = 20 A, and N = 300 turns for each coil. Place one coil in the yz plane with its center at the origin and the other in a parallel plane at x = 10 cm.

(a) Calculate the resultant field Bx at x = 5 cm, x = 7 cm, x = 9 cm, and x = 11 cm.

(b) Use your results and the fact that Bx is symmetric about the midpoint of the coils to sketch Bx versus x.