Linear and angular momentum stored in a distribution of charges in a magnetic field. The other side of the story - Torres del Castillo, Gerardo Francisco; Mendoza-Luna, Claudia Elizabeth (Revista Mexicana de Física E, 2025)
The linear or the angular momentum stored in an arbitrary electric charge distribution in the presence of a magnetic field is defined by calculating the linear or the angular momentum transferred to the electric charge distribution by a time-dependent magnetic field, which is initially zero and after some time reaches the desired final value. The component of the transferred linear momentum along some axis depends only on the final magnetic field if and only if the magnetic field is invariant under translations along this axis. Similarly, the component of the transferred angular momentum along some axis depends only on the final magnetic field if and only if the magnetic field is invariant under rotations about this axis.