Loop and Hertzian dipoles. In Problem 18.23 assume the currents in the dipole and in the loop are I1 and I2, but they are in phase.

(a) Find the polarization of the field in the far field.

b) Suppose the current in the loop and in the dipole are individually adjustable, but their phase is fixed. What are the types of polarization that may be achieved?

(c) Suppose the currents in the loop and Hertzian dipole remain constant in magnitude, but their phases may be changed individually. What are the types of polarization achievable?

Problem 18.23

Loop and Hertzian dipoles. An antenna is built as a combination of a Hertzian dipole of length 0.01A and a small loop of diameter 0.05λ. The dipole is placed at the center of the loop so that the plane of the loop is perpendicular to the dipole, at its center (see Figure 18.44). The two antennas are driven at 100 MHz with a current of magnitude I0 = 0.1A. For convenience place the loop on the xy plane at z = 0 and the dipole on the z axis, centered about the xy plane.

(a) Find the electric and magnetic fields in the far field if the currents in the antenna are in phase.

(b) Find the electric and magnetic fields in the far field if the current in the loop lags behind the current in the dipole by 1800.