Converse magnetoelectricity (Q) is the property describing the induced magnetization (M, the response) that occurs when an electric field (E, the stimulus) is applied to a material.

a) Write a tensor equation (with appropriate subscripts) defining this stimulus-response relationship that defines converse magnetoelectricity (Q).

b) From your knowledge of how M and E transform when the coordinate system is changed (under a transformation described by a direction cosine matrix a), prove how Q transforms. The resulting way that Q transforms defines the rank of the Q tensor.

c) What is the rank and type (polar or axial) of each of the tensors involved in your equation in part (a)?

d) How many tensor coefficients make up the Q tensor?

e) Give the equation for one component (your choice of which one) of the induced magnetization in terms of the applied electric field and relevant converse magnetoelectric coefficients.