Page 1 Module I: Electromagnetic waves Lecture 3: Time dependent EM ?elds: relaxation, propagation Amol Dighe TIFR, Mumbai Page 2 Module I: Electromagnetic waves Lecture 3: Time dependent EM ?elds: relaxation, propagation Amol Dighe TIFR, Mumbai Outline Relaxation to a stationary state Electromagnetic waves Propagating plane wave Decaying plane wave Page 3 Module I: Electromagnetic waves Lecture 3: Time dependent EM ?elds: relaxation, propagation Amol Dighe TIFR, Mumbai Outline Relaxation to a stationary state Electromagnetic waves Propagating plane wave Decaying plane wave Coming up... Relaxation to a stationary state Electromagnetic waves Propagating plane wave Decaying plane wave Page 4 Module I: Electromagnetic waves Lecture 3: Time dependent EM ?elds: relaxation, propagation Amol Dighe TIFR, Mumbai Outline Relaxation to a stationary state Electromagnetic waves Propagating plane wave Decaying plane wave Coming up... Relaxation to a stationary state Electromagnetic waves Propagating plane wave Decaying plane wave Stationary and non-stationary states I Stationary state, by de?nition, means that the currents are steady and there is no net charge movement, i.e. r ~ J s = 0 or @ @t = 0 (1) These statements are equivalent, due to continuity. I If the initial distribution of charges and currents does not satisfy the above criteria, they will redistribute themselves so that a stationary state is reached. I This process of “relaxation” happens over a time scale that is characteristic of the medium, called the relaxation time. Page 5 Module I: Electromagnetic waves Lecture 3: Time dependent EM ?elds: relaxation, propagation Amol Dighe TIFR, Mumbai Outline Relaxation to a stationary state Electromagnetic waves Propagating plane wave Decaying plane wave Coming up... Relaxation to a stationary state Electromagnetic waves Propagating plane wave Decaying plane wave Stationary and non-stationary states I Stationary state, by de?nition, means that the currents are steady and there is no net charge movement, i.e. r ~ J s = 0 or @ @t = 0 (1) These statements are equivalent, due to continuity. I If the initial distribution of charges and currents does not satisfy the above criteria, they will redistribute themselves so that a stationary state is reached. I This process of “relaxation” happens over a time scale that is characteristic of the medium, called the relaxation time. Relaxation time I The continuity equation, combining withr ~ D =, gives r @ ~ D @t =r ~ J (2) I Using ~ D = ~ E and ~ J = ~ E, r(1+ @ @t ) ~ J = 0 (3) I The solution to this differential equation is ~ J = ~ J s +( ~ J 0 ~ J s )e t= (4) where J 0 is the initial current distribution I == is the relaxation time I @ @t =r ~ J, ~ E = ~ J=, etc. relax at the same rate.Read More

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