On electromagnetic momentum of an electric dipole in a magnetic field

Abstract

The total linear electromagnetic field momentum $\mathbf P_{\mathrm{em}}$ of a stationary electric dipole $\mathbf p$ in a static magnetic field $\mathbf B$ is considered. The expression $\mathbf P_{\mathrm{em}} = \frac12\mathbf B \times \mathbf p$, which has previously been implied to hold in all static magnetic field situations, is not valid in general. The contribution of the electromagnetic momentum of the fringing fields of the dipole is discussed. It is shown that when either the static magnetic field or the electric dipole moment is changed, the mechanical impulse on the system equals $-\Delta\mathbf P_{\mathrm{em}}$, and hidden momentum does not need to be invoked in order to conserve total momentum.