In this work, an analytical expression is derived for the radial distribution of the quasi-static vertical magnetic field of a current-carrying large circular loop placed on a homogeneous earth. The obtained expression results from applying a rigorous procedure, which leads to cast the Hankel transform describing the vertical magnetic field component into a form consisting of two elliptic integrals and a fast-convergent sum of spherical Hankel functions. The derived solution ensures the same degree of accuracy as the finite difference time domain method, but, as a purely analytical formula, has the advantage of requiring less computational time. Numerical results are presented to illustrate the validity of the developed formulation.
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