By Arnold Sommerfeld, Edward G. Ramberg
Within the 3rd of a six-volume sequence, Sommerfeld offers a distillation of his lecture notes on electrodynamics.
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Extra resources for Electrodynamics. Lectures on Theoretical Physics, Vol. 3
E2 = ? (Ei - E,)2, (9) or expanded ΪΓ # = ! 2 £ Ϊ + ! Α Ϊ - ε Β τ Ε , . (9a) The last expression on the right is the mixed term mentioned above, while the first two terms denote the electric energy of the individual fields 1 and 2. However, we shall not need this expanded form and shall refer below to the representation in (9). 11a CONSERVATION OF ENERGY AND POYNTING VECTOR 31 tity W in (7a) represents a definitely positive quadratic form, formed with the components of the difference field E, H.
G. in the form (7a), applies formally also for them. However, the quantities W> S, WJy because of their quadratic character, are composed not merely of the cor responding quantities of the individual fields 1 and 2, but also of mixed terms involving 1 and 2. We show this for the quantity We as example, assuming isotropy for the sake of brevity. We = £ E D = ? E2 = ? (Ei - E,)2, (9) or expanded ΪΓ # = ! 2 £ Ϊ + ! Α Ϊ - ε Β τ Ε , . (9a) The last expression on the right is the mixed term mentioned above, while the first two terms denote the electric energy of the individual fields 1 and 2.
T within and outside of the coil and Hz = 0 outside of the coil, only one side of the loop contributes to the line integral. We find HI = Nili, H = NJ. (14) The magnetic excitation within the coil is given by the "number of ampere turns per unit length" NJ. This explains the designation of H customary in engineering practice which was introduced on p. 12. The value of H given by Eq. e. the same throughout the interior of the coil. §5. Law of Conservation of Energy and Poynting Vector Starting from Eqs.
Electrodynamics. Lectures on Theoretical Physics, Vol. 3 by Arnold Sommerfeld, Edward G. Ramberg