The fundamental axisymmetric boundary value problem of a single vortex penetrating a half-space of a type-II superconductor is investigated. From the appropriate static solution, closed form results are developed for all electromagnetic fields and densities within the superconductor. For the half-space above the superconductor, closed form results are obtained for all quantities with the introduction of a sole Laplace transformation. These results provide the analytic evaluation of a wide variety of derived quantities including magnetic moment, energy, and flux. The discussion has specific applications to magnetic force microscopy and other probe techniques.