Question

Question 2: For an electromagnetic plane wave, the electric field is given by: Ē= E, cos(kz +wt) ĉ +0 ġ+02 a) Determine the direction of propagation of the electromagnetic wave. b) Find the magnitude and direction of the magnetic field for the given electromagnetic wave B. c) Calculate the Poynting vector associated with this electromagnetic wave. What direction does this vector point? Does this makes sense? d) If the amplitude of the magnetic field was measured to be 2.5 * 10-7T, determine numerical values for the amplitude of the electric field and the Poynting vector.

Answer 1

ware The equeton of electre keld of the es given by E = Eo esn (k2 twt) in to 7 to 2 rato con (k twt) a (Q) n o indicates that witration of electric field en along There was of a term with the R ware Pro pagation vector k. This enda indicates that, the wave prospagetting Here n axas along az axus.

G u Now, the equation of plane wave propagething asse along thanen 6 &= Aser (wit - ka) So, coffe crent of (-k) endreeter the direction of propagation È = E, con Here the equation of electre Sield en z twt) a Bo con Twtt +64) (-2)] Sor the coefficrent of (k) en €2) so the EM wave prespagetting along - ve axin. (Amin) (6) Now a The es propagetting abry 2 exer. We know that, the con product of I and one. (Exo) directs the pro pagal on direction. So must must be along - y oxen no that (XB) along es along wave 2 ar le the maximum Now, let Boa amplitude of maps magnetic foold.

If e be the velocaley of light then we know that, Eo o 0 B. in the magnitude с Then of Rosso magnete field, directing along - y axend as cleos oübed earlier). But Son equation of magnete field en Bo can (kz <Z twt) (-9) (fo) con (kz twt) (9) B = B (6) Pogniting vectss es desened an- & tex Blava IRĒxe) [227 & overge value Ho < En con (kz+wx)]> [e." con (k2 tunt) (7)]) Lo con (k2 & wt) & Bo con (witt (22) х <E, B. con? (wt +xz) (-2) EoBo can? (wit + tez]> (-2)

(Reg 2 4 ro and Bo have content value, se are make them out of the arorge veloce opereton too Now, like and are rage od of Rap banden 2 Ad zin 2x or conra funnction du . L cos? (wt tiez)) = -2 Putting in equation 32 E B 3 en ¥ § (-2) 2 Eo Bo 2 м. - to 2o 튿 () (2) (2) [ (?) Vasco 3 E 2 We know that ملله C= で d. to cart Writo Then are two forms of poenting vector This poenta towards fra free space peini tuets - 8.85 axo chern 2. fm)

in This thin the direction of propagation of ed EM ware. This basically encicates the energy flow by the wave Move generelly et endeceler the interlity. (d) driver Bo= 2.5410 I T know that, B. Iy2x168 O for Boxe = 2.9416 - ZG Me From the nemmebrucal value of petrting pointing vector is, 1313 2 Moe (as)? 2x 40 r107x3x108 tools 7.46 W/m2- "Then the required value of painting vects r. A fm)
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