Hi, so the four-dimensional generalization of
$$\vec{B}=\mu\vec{H}$$
is
$$F_{\lambda \mu}u_{\nu} + F_{\mu \nu}u_{\lambda} + F_{\nu \lambda}u_{\mu} = \mu (H_{\lambda \mu}u_{\nu} + H_{\mu \nu}u_{\lambda} + H_{\nu \lambda}u_{\mu})$$
From these four-tensors and four-vector I should be able to...