In reading the instruction manual that came with your garage-door opener, you se

Question

In reading the instruction manual that came with your garage-door opener, you see that the transmitter unit in your car produces a 250 mW signal and that the receiver unit is supposed to respond to a radio wave of the correct frequency if the electric field amplitude exceeds 0.10 V/m . You wonder if this is really true. To find out, you put fresh batteries in the transmitter and start walking away from your garage while opening and closing the door. Your garage door finally fails to respond when you're 42 m away.

Are the manufacturer's claims true?
(a) yes
or
(b) no

Explanation / Answer

The energy flux of the EM field produced, which is equal to the intensity of the wave, by your radio transmitter is

<S> = oc/2 * E^2 = I = P/A

The EM wave is produce spherically, so the A = 4r^2, so let's see if the E field at r = 42m is equal to the minimum (0.1 V/m):

E^2 = P/Aoc = (250*10^-3 W)/( 4(42m)^2 * 8.85*10^-12 F/m * 3*10^8 m/s) = 0.14 V/m

So I would say yes, the manufacturer's claims are true, because it's the right number if you round it.

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