Question

1. Magnetic field in free space obeys the dependence i = 0.1(4ä, +38,) sin (wt - 2.10%(-3x + 4y)) in the St units. A) What are the wave vector and the frequency w?: B)Show that this dependence is consistent with Maxwell equations for the plane wave; C) Use the phasor method and find the electric field of this wave.

Answer 1

Soll Data given in the Tuestion is as follows: A) Magnetic field Intensity in free in free space is given by H = 0.1 - (hann + 367) Sin [wt-2 -27 X10(-3x+4y D Compore equation ③ Keith Standard expression as- H Ho Sin (cut-Br) Hence, the Propotion Vector is given as. - 36 tha Bra + 21 XL05 (- 31 th)) hare Vector B- 24X108 (-395 + hy) 29 +16 Brz 27X105 (-3 en +4%) 5 L kere Vector | Brl= 25x105x d9+16 1 Bl= 24 x 105 x5=10 7XL05 BH = 10tx 105

We know the the Relation between Velocity and Phose Constant Bin free space is giren by - 3x108- W lonxlos 30tx 103 Rod = 305x1013 Rad/sec Hence, the frequency CW=305x103 Rad/see ② Ashee hare giren- H = 0.2 (hann + 30%) Sin fact- 27 xlos (-surly)] T fiend rector Plone Veeter hart af Z E Here field vector = 3a Plone Vector = - 3am thay Dependence of above equation is said to be consistant with Moxhen equation if

Hence- af ap = (hau + 307) (-300 + 465) af- op - - 12 +12 O Hence, the above equation is said to be consistent. We know that, the Relation between the electric field And Magnetic freed is given by En ĦX 120 T Q8 = Propagation Vecter = (-3an't Where N = Intrinsic Impedance of free space F = Magnetic field Intensity - 499) E = electric field Intensity Now Subsituating the above values in equation ③ leeget- E = 1201 x 0.1 (42@ +389) Sin (wt - 2n xiom (<39 +4y)] *[czem ten E = 12m sin [wt- 20 x103 (ranray) Chan1 309) x Gaant 46) È = 126 Sin Teuf - 25x1d(<3n thy]] [16 Q2 +924) 300 sin [ue- 2 + x103 (-anthy)] Gå Cons of the arenas