A turnstile antenna consists of two crossed dipole antennas, positioned in this case in the xy plane. The dipoles are identical, lie along the x and y axes, and are both fed at the origin. Assume that equal currents are supplied to each antenna and that a zero phase reference is applied to the x-directed antenna. Determine the relative phase, ξ, of the y-directed antenna so that the net radiated electric field as measured on the positive z axis is

(a) Left circularly polarized;

(b) Linearly polarized along the 45◦ axis between x and y.