Metal sphere in the field of an alternating current loop

A solution is obtained to the problem of diffraction of the electromagnetic wave of an annular alternating (harmonic) current by a conducting metallic sphere. The method of variation of constants is used to derive series expressions for the components of the electric and magnetic field both inside and outside the sphere. Formulas are presented for the summation of Legendre function of the second kind in terms of Gegenbauer polynomials, which makes it possible to sum the relevant series and to present the field components in compact finite form at low and high frequencies. The components of the electromagnetic field are presented in integral form.