Waves: determining the max distance of a traveling wave

[Barry Melby]

You want to build a portable device that can detect pirate radio stations broadcasting at about 50 W of power a few miles from your beachfront home. You have a 0.60-m diameter bowl you might use as an antenna dish, but you are worried that your amplifier input will require a signal of at least 0.10 μW. Determine the maximum distance from a radio station at which the signal would still be sufficient for you to detect it with your dish.

I believe that you should be using the following equations: I = P/A = P/(4*pi*r^2) & I_surf = P/L

I attempted to find the solution by solving for I when P = 50 W and A = 4*pi*(.30)^2 then plugging I into the second equation, but this isn't giving me the correct results. Where am I going wrong here?

 

[SteamKing]

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