Poynting's theorem

In electrodynamics, Poynting's theorem is a statement of conservation of energy for the electromagnetic field, in the form of a partial differential equation, due to the British physicist John Henry Poynting. Poynting's theorem is analogous to the work-energy theorem in classical mechanics, and mathematically similar to the continuity equation, because it relates the energy stored in the electromagnetic field to the work done on a charge distribution (i.e. an electrically charged object), through energy flux. − ∂ u ∂ t = ∇ ⋅ S + J ⋅ E {displaystyle -{frac {partial u}{partial t}}= abla cdot mathbf {S} +mathbf {J} cdot mathbf {E} } − ∂ ∂ t ∫ V u d V = {displaystyle -{frac {partial }{partial t}}int _{V}udV=} ∂ V {displaystyle scriptstyle partial V} S ⋅ d A + ∫ V J ⋅ E d V {displaystyle mathbf {S} cdot dmathbf {A} +int _{V}mathbf {J} cdot mathbf {E} dV} where ρ is the charge density of the distribution and v its velocity. Since J = ρ v {displaystyle mathbf {J} = ho mathbf {v} } , the rate of work done by the force is In electrodynamics, Poynting's theorem is a statement of conservation of energy for the electromagnetic field, in the form of a partial differential equation, due to the British physicist John Henry Poynting. Poynting's theorem is analogous to the work-energy theorem in classical mechanics, and mathematically similar to the continuity equation, because it relates the energy stored in the electromagnetic field to the work done on a charge distribution (i.e. an electrically charged object), through energy flux.