1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    curl E= dB/dt
    --------------- relation H and B---
    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted