You bought and installed a new garage-door opener. The manual claims that the tr

Question

You bought and installed a new garage-door opener. The manual claims that the transmitter (the one you hold and press its button) produces a 250 mW signal while the receiver (in the garage) is supposed to respond if the radio wave has electric field amplitude exceeding 0.1 V/m. You are skeptical about these numbers, and decide to do an experiment. You put fresh batteries in the transmitter and start walking away from the garage while opening and closing the garage door. The garage door opener fails to respond when you are 42 m away. Are the manufacturers numbers correct?

Explanation / Answer

calculate the E field at the given distance:

Intensity = power / 4pi dist^2 = 0.250 / 4pi*42^2 =

        = 1.1278 x 10^-5

Now...

   E^2 = intensity * 240 pi = 1.1278 x 10^-5 * 240 * pi =

           = 0.0085034

   E = 0.0922 V/m

It appears the numbers are approx correct. The field when the transmitter stopped working was about 0.09 V/m, which is slightly less than the given value of 0.10 V/m

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