Exact expression for the magnetic field of a finite cylinder with arbitrary uniform magnetization

An exact analytical expression for the magnetic field of a cylinder of finite length with a uniform, transverse magnetization is derived. Together with known expressions for the magnetic field due to longitudinal magnetization, the calculation of magnetic fields for cylinders with an arbitrary magnetization direction is possible. The expression for transverse magnetization is validated successfully against the well-known limits of an infinitely long cylinder, the field on the axis of the cylinder and in the far field limit. Comparison with a numerical finite-element method displays good agreement, making the advantage of an analytical method over grid-based methods evident.