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Poynting Vector Problem

  1. Nov 22, 2015 #1
    1. The problem statement, all variables and given/known data
    In free space, the electric field of a plane EM wave is given by: E(z,t)= 50î cos[wt-kz]
    where w= 6 x 10^15
    and k=2x10^7
    (A) calculate the amplitude of the magnetic field H
    How much energy does this wave transmit in 30s when it passes through a window of dimensions 2mx3m if the EM wave is incident:
    (b) normally on the window
    (c) obliquely at an angle of 30 degrees with respect to the window normal
    2. Relevant equations
    Maxwell:
    curl E= dB/dt
    --------------- relation H and B---
    H=B/mu0
    mu0=4pi x 10 ^-7
    ----------------------------------------
    3. The attempt at a solution
    For (A) I relate the two fields via the Maxwell curl E= dB/dt which yields:
    50k j cos(wt-kz) = w B
    such that B= 50k/w cos (wt-kz)
    the amplitude becomes 50k/w=(10^9)/(6x10^15)= 1/6 x 10^-6
    now relate this to H=B/mu0 ---> (1/6 x 10^-6)/(4pi x 10^-7)= (10/6) / (4pi) =0.13 A/m

    did I d (A) correclty, does the outcome make sense?
    Also, I have no clue how to do (b) and (c)?
     
  2. jcsd
  3. Nov 24, 2015 #2
  4. Nov 24, 2015 #3
    Okay so I found an equation for the average energy of a plane wave:

    <S>= Em2/(2 c μ0) where c is the speed of light, mu the magnetic permeability of free space, Em=50 in this case. <S> is the averaged Poyting vector, such that ENERGY=<S> *area* time, which gives me, when I plug in the numbers: (area =3x2, t=30s)

    for (b) I get: 0.597 kJ
    for (c) I get: Cos[π/6] *0.859=0.517 kJ

    *** I checked my Bm field of (a) by checking that Em/Bm=c=3x10^8, which it did, so I assume I can divide by mu naught correctly
     
    Last edited: Nov 24, 2015
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