The magnetic field on the axis of a circular current loop (eq. 5.41) is far from uniform (it falls off sharply with increasing z). you can produce a more nearly uniform field by using two such loops a distance d apart (fig. 5.59). (a) find the field (b) as a function of z, and show that ∂b/∂z is zero at the point midway between them (z = 0). (b) if you pick d just right, the second derivative of b will also vanish at the mid- point. this arrangement is known as a helmholtz coil; it’s a convenient way of producing relatively uniform fields in the laboratory. determine d such that ∂2 b/∂z2 = 0 at the midpoint, and find the resulting magnetic field at the center. √ [ 8μ0i/5 5r]