(a) Two rings of radius R, coaxial with the z-axis, are separated by a distance 2b and carry a current I in the same direction. Make explicit use of the formula for the magnetic field of a single current ring on its symmetry axis to derive the Helmholtz relation between b and R that makes B_z(z) most uniform in the neighborhood of the midpoint between the rings.
(b) Agradient coil has the same geometry as part (a) except that the rings carry current in opposite directions. Compute B_z(z) in the immediate vicinity of the midpoint between the rings for an arbitrary choice o the ring separation.