A pair of Helmholtz coils are often used in laboratories to produce magnetic fields. The coils consist of two rings of radius R on a common axis separated by a distance R. The rings carry equal currents in the same direction. Suppose that the coils are parallel to the X-Y plane and their centers are at Z =+ R/2. (a) Find the magnetic field Bz on the z-axis. (b) Show that at z = 0, the first, the second and the third derivatives vanish.

A pair of Helmholtz coils are often used in laboratories to produce magnetic fields. The coils consist of two rings of radius R on a common axis separated by a distance R. The rings carry equal currents in the same direction. Suppose that the coils are parallel to the X-Y plane and their centers are at Z =+ R/2. (a) Find the magnetic field Bz on the z-axis. (b) Show that at z = 0, the first, the second and the third derivatives vanish.