Lienard-Weichert potentials for an antenna

Is it possible to work out the Magnetic and electric fields of a loop antenna using the Lienard-Weichert potentials ? I would like a detailed derivation of how this is done

Electromagnetic theory

A circular current loop made of flexible wire is located in a magnetic field B; you may keep B constant or vary it. Describe three ways an emf can be induced in the loop.

The problem describes the technique of calculating magnetic flux, induced emf, current in a loop kept in a uniform magnetic field and undergoing some twist. It also calculates equation of motion.

A conducting loop of area A and total resistance R is suspended by a torsion spring of constant k in a uniform magnetic field B=B e_y. The loop is in the yz plane at equilibrium and can rotate about the z -axis with the moment of inertia I as shown in figure. The loop is displaced by a small angle Theta from equilibrium and released. Assume the torsion spring is non-conducting and neglect self-inductance of the loop. (a) What is the equation of motion for the loop in terms of the given parameters? (b) Sketch the motion and label all the relevant time scales for the case when R is very large.

This problem deals with interaction of charged particle bounded by Coulomb interaction accoridng to classical radiation theory.

A particle with mass m and electric charge q is bound by the Coulomb interaction to an infinitely massive particle with electric charge -q. At t=0 its orbit is (approximately) a circle of radius R. At what time will it have spiralled into R/2? (Assume that R is large enough so that you can use the classical radiation theory than quantum mechanics.)

On the invariance of Lorentz transformations.

Show that E^2-B^2 and vec{E}.vec{B} are invariant under a Lorentz transformation.