Two Helmholtz coils with radii R have their axes along the x axis (see Problem 17). One coil is in the yz plane and the other is in a parallel plane at x = R. Show that at the midpoint of the coils (x = ½R), dBx/dx = 0, d2Bx/dx2 = 0, and d3Bx/dx3 = 0. This shows that the magnetic field at points near the midpoint is approximately equal to that at the midpoint.