b If H sin t \u03b2 z \u02c6x A m \u03c3 0 \u03b2 2 3 c and 2 25 o find the corresponding E by

B if h sin t β z ˆx a m σ 0 β 2 3 c and 2 25 o

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b) IfH= sin(!t-βz) ˆxAm,σ= 0,!β=23cand= 2.25o, find the correspondingEby using Ampere’s lawr ⇥H=J+@D@tin whichJ=σEandD=E.6. Ay-polarized plane TEM wave is propagating in vacuum (i.e.,v=c3108m/s and=o120) in +xdirection.If the time variation of the wave field atx= 0 is described asEy(0, t) = 44(t) V/m, where= 4μs and4(t) is the unit triangle function with width,a) Determine the vector wavefieldE(x, t) written explicitly in terms of all space and time variablesxandt,b) Determine the accompanying wavefieldH(x, t) in A/m units,c) Determine the maximum value ofPoynting vectorEH.d) What trajectory functionx=x(t) describes instantaneous locations of the peak ofEH.e) PlotEy(x, t) vstatx= +1500 m.f) PlotHz(x, t) vsxatt= 12μs.7. In a homogeneous lossess dielectric with=roandμ=μrμoa plane TEM wave with the followingcomponents is observed:E= ˆxu(t-zc/2) + ˆyg(t-zc/2)VmandH= ˆx10zc-ˆx5t+ ˆy1120u(t-2zc)Am,whereu(t) denotes the unit-step function andcis the speed of light in free space. Using the aboveinformation,a) Determine the intrinsic impedancefor the medium.b) Determine the propagation velocityv.c) Determinerandμr.d) Functiong(t).8. For each of the four plane waves (in free space) described bya)E1= 4 cos(!t-βzxV/mb)E2=Eocos(!t+βzx-Eosin(!t+βzyc)H3= cos(!t+βz+3x+ sin(!t+βz-6yA/md)H4= cos(!t-βxz+ sin(!t-βxyA/m:i. Determine the expression forHorEthat accompanies the given wave field.ii. Find the expression for instantaneous power that crosses a 1 m2area in thexy-plane from-zto +z.iii. Find time averaged power that crosses a 1 m2area in thexy-plane from-zto +z. 3
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  • Summer '08
  • FRANKE
  • Electromagnet, Magnetic Field, Electric charge, inner loop, di↵erential equation

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