Magnetic brain stimulation: calculation of electric field induced by arbitrary shaped coils in spherical coordinate with time variable

It is very important in magnetic brain stimulation that knowing the induced electric field distribution. Because of its calculation complexity, spherical coordinate is used to replace rectangular coordinate in traditional method and simplify the calculation. In this paper, the induced electric fields stimulated by arbitrary coils are calculated based on sphere head model. In the past researches, time variable was neglected for simplification, but the electric field always varies with time. To depict it more precisely, the time variable is considered.