The boundary value problem posed is a truncated cylindrical region excited by a specified distribution of electric current over a concentric cylindrical surface. The end conditions are that the total normal current density is zero. The solution is carried through for excitation by a symmetrically located axial current filament that is adjacent to the cylinder. Numerical results of the resultant magnetic field are given for the quasi-static situation for a perfectly conducting cylinder. It is indicated that the results depend significantly on the length of the cylindrical target. Even for very long cylinders, there is no quantitative similarity with the corresponding two-dimensional model of a cylinder of infinite length.