Energy in Electromagnetic Waves: Classical and Quantum Perspectives - Prof. Phillip Duxbur, Study notes of Physics

Download Energy in Electromagnetic Waves: Classical and Quantum Perspectives - Prof. Phillip Duxbur and more Study notes Physics in PDF only on Docsity! PHY481 - Lecture 31 Section 10.3-10.5 of PS, Sections 7.2.3, 7.2.4 of Griffiths Energy in EM waves The classical EM energy density in vaccuum is composed of the electric and magnetic contributions, u = 1 2 0E 2 + 1 2µ0 B2 = 0E 2 = B2 µ0 = EB cµ0 (1) where the latter two expressions are found by using ~E = c ~B and c = (µ00) −1/2, and we only used the magnitudes of the fields. The energy flux density is the amount of energy crossing a surface per unit time. Lets consider a surface perpendicular to the direction of motion so that the amount of energy crossing a unit surface area is Energy flux density = length ∗ u/time = cu = EB µ0 (2) A compact way of writing this energy flux is to use the fact that the direction of propagation is the direction of ~E∧ ~B, so it is natural to define the vector quantity that gives the magnitude and direction of the Energy flux density, the Poynting vector ~S, ~S = 1 µ0 ~E ∧ ~B (3) Now lets consider the quantum mechanical understanding of EM waves. In that case we know that each photon carries energy hν, so the energy flux density is the number of photons per unit time per unit area multiplied by hν, Quantum energy flux density = nν(t)hν = Intensity = Power/area (4) where nν(t) is the number of photons arriving at a surface per unit area per unit time. Note that this is the average energy flux density, whereas the Poynting vector gives the instantaneous power per unit area so the intensity in the classical case is I = Sav, where Sav = E0B0/(2µ0) is the time average of the Poynting vector and E0, B0 are the peak values of the electric and magnetic fields respectively. 1