Radiation from a circular loop in the presence of spherically symmetric conducting or dielectric objects

The problem of electromagnetic radiation from a circular loop antenna of radius a, carrying a current I is considered. The loop may be radiating in the presence of one or more of the following objects: a centrally located dielectric or perfectly conducting sphere of radius b<a, a spherical dielectric shell of inner radius c>a and outer radius d, a perfectly conducting spherically symmetric cap at radius b, and another such cap at radius d. Typically geometric structures considered are shown. It is demonstrated how the presence of the sphere, shell, and caps can change and direct the radiation pattern of the loop