Isotropic Magnetoelectric Cylinder With Elliptical Cross Section Exposed to a Homogeneous Electric Field: An Analytical Solution

We derive an analytical solution for the electric and magnetic field inside and outside a long magnetoelectric (ME) cylinder with an elliptical cross section exposed to an external homogeneous electric field. The analytical solution is obtained using the method of separation of variables. The fields are compared to a finite element solution. We obtain a mean relative error in the cylinder below 0.6% and a normalized root mean square deviation (NRMSD) outside the cylinder below 0.11%. We show that a static solution for the electric and magnetic field inside the cylinder in a constant electric field is also constant. We also show that the electric field in the cylinder is not necessarily parallel to the external electric field; the parallelism occurs only in the case of a cylinder with a circular cross section. Our method can be used directly to compute the fields in magnetoelectric materials using an external electric field. Furthermore, it allows for direct inclusion into inverse solutions when determining unknown magnetoelectric parameters on the basis of measuring magnetic and electric fields in the near vicinity of a cylinder.