The author revisits the problem of a circular symmetric planar current embedded in a dielectric board and emphasizes a sufficient condition that a lossy board with negligible lateral faces equivalent currents, which can reduces the general surface integral equations (SIEs) over the finite-sized homogeneous dielectric board into coupled radial function integral equations that conform to be a satisfiable generalized simultaneous bounded linear operator equations on Hilbert spaces of countably infinite dimensions. The finalized infinite series solution is of guaranteed convergence and accuracy compared to the numerical solutions from the arbitrary geometry method of moments (MoM) (e.g., RWG-MoM) applied to solve the respective SIEs over thin board.