# Homework Help: Distance of hearing a radio station

1. Nov 16, 2008

### gillyr2

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. Nov 17, 2008

### gillyr2

can anybody help?

3. Nov 18, 2008

### mcdermott2

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!