Energy of a classical charged particle in an external electromagnetic field

For a classical nonrelativistic charged particle in an external time-dependent electromagnetic field the particle's energy is not in general the particle's Hamiltonian. A gauge-invariant energy is defined as the sum of the kinetic energy and the conservative potential energy. The rate of change of the particle's energy is equal to the power supplied to the particle by the external time-dependent electromagnetic field. The particle's energy is its Hamiltonian minus the scalar potential of the time-dependent electromagnetic field (multiplied by the charge).