This paper presents an analytical method for reconstructing the magnetic flux density (MFD) field around the rotor of a permanent magnet spherical motor (PMSM) using measured MFD on its surface, and for formulating the motor torque according to Lorentz's law. When reconstructing the MFD, the solutions to Laplace's equation of a magnetic scalar potential with measured boundary conditions (BCs) in the current-free space around the rotor are obtained using the method of separation of variables. The models yield precise MFD and torque solutions in closed form, and yet require no information on the magnetic structures and properties of the rotor. This advantage provides a good basis for model identification, calibration as well as for control of an electromagnetic actuator. Both the magnetic field and torque models have been validated by comparing against published experimental data, which show excellent agreement.