Near fields of the constant current thin circular loop antenna of arbitrary radius

Assuming a known (constant) current distribution on the thin circular loop antenna of arbitrary radius in free space, an exact integration of the vector potential is performed without recourse to approximations. The only restrictions on the solution variables are that the observation point distance must be greater than the loop radius and that the polar angle must run between 0 and pi. The resulting vector potential infinite series solution possesses a real part composed of linear combinations of complete elliptic integrals of the first and second kind and an imaginary part composed of elementary functions. Thus, it is possible to obtain an exact solution which is valid everywhere that r > a and 0 less than or equal to theta less than or equal to pi. The electromagnetic field components of the constant current circular loop antenna are then determined by direct series differentiation. These solutions are valid in the near and induction fields, converging rapidly there, and are also valid in the far field, although many terms of the series are needed for convergence.