On the dynamics of electromagnetic bodies

The electromagnetic fields in a vacuum or in a body are ruled by the Maxwell equations. The mechanical behaviour of materials is governed by the balance equations of mechanics, which are possibly coupled with the Maxwell equations. Notions such as stress and momentum can be associated with the electromagnetic fields. Unfortunately, there is no general agreement on the proper form that these quantities should have in a material body. However, if the equations of mechanics and the Maxwell equations are consistently derived from a general principle, stresses and momenta are properly selected in a natural way. In this context, the electromagnetic Eshelby tensor is also introduced in a natural way.