A rectangular coil is composed of 150 turns of a filamentary conductor. Find the mutual inductance in free space between this coil and an infinite straight filament on the z axis if the four corners of the coil are located at:

(a) (0, 1, 0), (0, 3, 0), (0, 3, 1), and (0, 1, 1);

(b) (1, 1, 0), (1, 3, 0), (1, 3, 1), and (1, 1, 1).