# poynting - The Poynting vector: power and energy in...

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The Poynting vector: power and energy inelectromagnetic fieldsKenneth H. CarpenterDepartment of Electrical and Computer EngineeringKansas State UniversityOctober 19, 20041Conservation of energy in electromagneticsThe concept ofconservation of energy(along withconservation of momen-tum) is one of the basic principles of physics – both classical and modern.When dealing with electromagnetic fields a way is needed to relate the con-cept of energy to the fields. This is done by means of the Poynting vector:P=E×H.(1)In eq.(1)Eis the electric field intensity,His the magnetic field intensity,andPis the Poynting vector, which is found to be the power density inthe electromagnetic field. The conservation of energy is then established bymeans of the Poynting theorem.2The Poynting theoremBy using the Maxwell equations for the curl of the fields along with Gauss’sdivergence theorem and an identity from vector analysis, we may prove whatis known as thePoynting theorem.

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