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? Yes or no?

Explanation / Answer

Intensity = Power/Area

Intensity = 250 * 10^-3 / 4*pi*(42)^2 = 0.000011277 W/m^2

E = sqrt(Intensity*Z0) =sqrt(376.73*0.000011277)

where Z0 = 376.73 ohms

E = 0.065 V/m

Now for E to increase the user must come closer to the door rather than going away.

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