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Robot Lawn Mowers have those Boundary Wires where a weak current runs through which creates a magnetic field around it. The Robot then detects the magnetic field and knows it reached the end of the lawn. I want to use the same system to navigate my robot.

I did some calculation which I'm not sure about if I did it right

If I run 100mA through the wire I create a magnetic field of 1.33*10^-7T at a distance of 15cm away from the wire. Isn't this far to little to get detected by any magnetic field sensor? How are the robot lawn mowers able to measure that magnetic field?

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A quick internet search for "how does Robot Lawn Mower detect Boundary Wire" turned up a patent which suggests that the mower knows what it's looking for. That is, the transmitter sends a signal with fancy coding. The receiver can use its knowledge of the coding scheme, plus its own fancy signal processing, to pull the signal out of the noise. Of course, no particular mower has to use exactly that scheme.

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