Please answer all parts!

a. Evaluate the total magnetic field on the z axis, i.e. determine B(z) for any d value. OBz b. Show that for any d, az = 0. Thus, the the magnetic field is at either a minimum or |z=0 maximum (as a function of z) at z = 0. c. Show that for d = R, 2z2 = 0. Thus, the magnetic field at the midpoint between the =0 two rings is the most uniform when d = R. d. Suppose d # R. Under what conditions on d is the field maximum at z = 0. Conversely, under what conditions is the field at a minimum at z = 0.\"Helmholtz Coils\" is a term for a particular arrangement of two circular loops of current normal to, and centered on, the z axis with a particular spacing, d, such that one loop is at z = +d/ 2 and the other is at z = d/ 2. The loops have radius, R, and carry a counter-clockwise current. z='d/2 z'=0 zed/2 The Helmholtz arrangement corresponds to d = R