4) [20 points] The Helmholz coil is a pair of circular current loops of radius a with a common axis, separated by a distance 26 which is chosen to make the second derivative of B vanish at a distance at a point on the axis halfway between the two coils. Show that this distance is 2b a and also find the coefficient C in the Taylor expansion = Bz(b+8) = Bz(b)(1 + C() 4 + +...]. a (3) You'll probably have to start by finding B for a single coil along its axis; this is simple Biot-Savart cranking. This problem is a bit messy but if you are a table top experimentalist you might actually use Helmholz coils someday.