Clearly, the larger the strength of the electric and magnetic fields, the more work they can do and the greater the energy the electromagnetic wave carries. non-interacting field) can be expressed as the Fourier sum of creation and annihilation operators in energy-momentum space while the effects of the interacting quantum field may be analyzed in perturbation theory via the S-matrix with the aid of a whole host of mathematical technologies such as the Dyson series, Wick's theorem, correlation functions, time-evolution operators, Feynman diagrams etc. The power flows with a density S (watts/m2), a vector, so that the power crossing a surface Sa is given by Sa Mathematical descriptions of the electromagnetic field, A Dynamical Theory of the Electromagnetic Field, National Institute for Occupational Safety and Health, Quantization of the electromagnetic field, "NIOSH Fact Sheet: EMFs in the Workplace", "Electromagnetic fields: key topics and projects", Non-Ionizing Radiation, Part 1: Static and Extremely Low-Frequency (ELF) Electric and Magnetic Fields (2002), National Institute for Occupational Safety and Health – EMF Topic Page, Biological Effects of Power Frequency Electric and Magnetic Fields (May 1989), https://en.wikipedia.org/w/index.php?title=Electromagnetic_field&oldid=987359701, Short description is different from Wikidata, Articles with unsourced statements from May 2011, Articles with unsourced statements from August 2015, Creative Commons Attribution-ShareAlike License. But there is energy in an electromagnetic wave, whether it is absorbed or not. The divergence of the stress–energy tensor is: where ) In a field, theoretical generalization, the energy must be imagined dis tributed through space with an energy density W (joules/m3), and the power is dissipated at a local rate of dissipation per unit volume Pd (watts/m3). Ampere's Law roughly states that 'a changing electric field creates a magnetic field'. where J f is the current density of free charges and u is the electromagnetic energy density for linear, nondispersive materials, given by = (⋅ + ⋅), where E is the electric field; D is the electric displacement field; B is the magnetic field; H is the magnetic auxiliary field. Until 1820, when the Danish physicist H. C. Ørsted showed the effect of electric current on a compass needle, electricity and magnetism had been viewed as unrelated phenomena. Often only the useful or extractable energy is measured, which is to say that inaccessible energy (such as rest mass energy) is ignored. With electromagnetic waves, as with other waves, there is an associated energy density and energy flux. ν This equation is equivalent to the following 3D conservation laws, respectively describing the flux of electromagnetic energy density.