When interacting with a large biopolymer or even larger organelle, a small molecule might not rotate freely in all directions and the dipolar interaction might not average to zero. Suppose a molecule is bound so that, although the vector separating two protons may rotate freely around the zaxis, the colatitudes may vary only between 0 and 8'. Average the dipolar field over this restricted range of orientations and confirm that the average vanishes when 8' =11: (corresponding to rotation over an entire sphere). What is the average value of the local dipolar field for the H20 molecule in Problem 15.15 if it is bound to a biopolymer that enables it to rotate up to 8' = 30°?