  We propose dynamic non-linear equations for moving surfaces in
electromagnetic field. The field is induced by a material body with a boundary
of the surface. Correspondingly the potential energy, set by the field at the
boundary, can be written as an addition of four-potential times four-current to
a contraction of electromagnetic tensor. Proper application of minimal action
principle to the system Lagrangian yields dynamic non-linear equations for
moving three dimensional manifolds in electromagnetic fields. The equations, in
different conditions simplify to Maxwell equations for massless three surfaces,
to Euler equations for dynamic fluid, to magneto-hydrodynamic equations and to
Poisson-Boltzmann equation. To illustrate effectiveness of the equations of
motion we apply the formalism to analyze dynamics of macro-molecules and
membranes.
