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E/M waves What do charges have to do to create E/M radiation? Accelerate! A Radiation from a single dipole P1. Suppose that the two charges are moving apart at this time. What is the direction of 0 E (displacement t current) at the center? a) Up b) down P2. What is the direction of induced B at point A ? a) out of page b) into page c) right d) left E B 0 J 0 0 t path A B dl o I piercing surface d ˆ o o E ndA dt open surface bounded by path Radiation from a single dipole B E t P3. What is the direction of the curl of E near point A if B is increasing? a) out of page b) into page c) right d) left A Radiation from a single dipole B E t Inside the atom where e- is moving: E B 0 J 0 0 t After light has left the atoms (vacuum): E B 0 0 t Far from the dipole the field lines straighten into plane waves E r , t Eo e i k r t B r , t Bo e i k r t What does physically? Eo e i k r t mean Review phasors Two ways to indicate phase of wave Beauty of using exponentials in uniform plane waves i k x x k y y k z z t Eo e t i k x x k y y k z z t Eo e x A E 0 2 (remember these relations) E vs B Direction E r , t Eo e i k r t Magnitude B r , t Bo e Phase Bo i k r t A (remember the ratio of Eo/Bo in a plane wave) Dipole radidation, antennas The greatest intensity is _______ to the line of acceleration. Index of refraction from polarization 2 2 J E P 2 P E o o o o 2 2 t t t n 1 Assumption of a linear medium (learn this derivation of n) k v 2 c A vac f n 2 f n 2 n k vac n Demo: waves in 1-D: wavelength, curvature vs wave speed. http://phet.colorado.edu/sims/wave-ona-string/wave-on-a-string_en.html c Review P. f ( x, t) f ( x ct)is a solution to It is also a solution to ____: 1) 3 1 3 f ( x, t) x 2) a) b) c) d) 3 f ( x, t) c 3 t 3 0 4 1 4 f ( x, t) f ( x, t) 4 0 4 4 x c t eqn 1 eqn 2 both neither 2 1 2 f ( x, t) f ( x, t) 2 0 2 2 x c t