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The Poynting theorem is a statement due to John Henry Poynting about the conservation of energy for the electromagnetic field. It relates the time derivative of the energy density, u, to the energy flow and the rate at which the fields do work. It is summarised by the following formula
- <math>\frac{\partial u}{\partial t} + \nabla\cdot\mathbf{S} = -\mathbf{J}\cdot\mathbf{E}<math>
where S is the Poynting vector representing the flow of energy, J is the current density and E is the electric field. Since the magnetic field does no work, the right hand side gives the total work done by the electromagnetic field.
See also
Poynting flux, Poynting vector
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