The magnetic scalar potential and demagnetization vector for a cylinder tile

A closed-form solution for the magnetic scalar potential generated by a uniformly magnetized cylindrical slice and a full cylinder is determined by solving Poisson’s equation analytically. The solution is given in terms of elliptic integrals of the first, second and third kind. We show that the magnetic scalar potential can be written as the dot product of a demagnetization vector, containing all the geometric information of the generating cylinder, and the magnetization. We validate the derived analytical expressions for the magnetic scalar potential by comparing with a finite element simulation and show that these agree perfectly for both the cylindrical slice and the full cylinder.