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Homework Help: Distance of hearing a radio station

  1. Nov 16, 2008 #1
    1. The problem statement, all variables and given/known data
    A radio station is allowed to broadcast at an average power not to exceed 24 kW.
    If an electric field amplitude of 2.6×10−2 V/m is considered to be acceptable for receiving the radio transmission, estimate how many kilometers away you might be able to hear this station.


    2. Relevant equations

    P/A = e_0*c*E^2

    3. The attempt at a solution

    e_0*c*E^2/P = 1/pi r^2

    sqrt(24000/(8.85 *10^-12*3*10^8*pi)) = 65.2 km

    help!
     
  2. jcsd
  3. Nov 17, 2008 #2
    can anybody help?
     
  4. Nov 18, 2008 #3
    I just had this problem and this is how I solved it

    S=P/A where S=(.5)c(permittivity of free space)(E^2) - (this is the average value of S not an instantaneous value. Your equation for S was assuming the instantaneous value)

    then a little rearranging:

    A=P/S
    (4)(pi)(r^2)=P/S - (4pir^2 is the surface area of a sphere, I think you were incorrectly using the area of a circle)

    you should be able to solve from here!
     
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