Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/368

 or the same way as dynamical energy is carried by water flowing in a pipe; whereas in Maxwell's theory, the storehouse and vehicle of energy is the dielectric medium surrounding the wire. What Poynting achieved was to show that the flux of energy at any place might be expressed by a simple formula in terms of the electric and magnetic forces at the place.

Denoting as usual by the electric force, by  the electric displacement, by  the magnetic force, and by  the magnetic induction, the energy stored in unit volume of the medium is  so the increase of this in unit time is (since in isotropic media  is proportional to, and  is proportional to )

or where denotes the total current, and  the current of conduction; or (in virtue of the fundamental electromagnetic equations)

or Now is the amount of electric energy transformed into heat per unit volume per second; and therefore the quantity  must represent the deposit of energy in unit volume per second due to the streaming of energy; which shows that the flux of energy is represented by the vector. This is Poynting's theorem: that the flux of energy at any place is represented by the vector-product of the electric and magnetic forces, divided by 4π.