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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 calculations and I'm not sure 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 too 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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    \$\begingroup\$ It's probably an AC magnetic field detected by a sensor tuned to the specific frequency. \$\endgroup\$ Commented Sep 22, 2022 at 14:37
  • \$\begingroup\$ If you have access to a little lab equipment, I'd recommend you to do the experiment yourself. Connect a loop of wire to a function generator, set it to say 100 kHz square wave output, something like 5-10Vp-p. Then find a small inductor of a few µH and connect that to an oscilloscope. You'll have no problems detecting the signal with the oscilloscope. The lawn mower basically does the same thing. \$\endgroup\$
    – Klas-Kenny
    Commented Sep 22, 2022 at 14:54
  • \$\begingroup\$ Do lawn mowers change direction at 15cm from the wire or closer? \$\endgroup\$
    – Solar Mike
    Commented Sep 22, 2022 at 14:57
  • \$\begingroup\$ Thanks for all your comments. I have access to lab equipment so I will try it. \$\endgroup\$
    – Linus
    Commented Sep 22, 2022 at 15:01
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    \$\begingroup\$ "When I brought the inductor close to the wire nothing changed." How were you measuring? What was the orientation of the coil relative to the wire? Did you have a core in the inductor? If so, was it toroidal or bar? Add the information into your question. \$\endgroup\$
    – Transistor
    Commented Sep 22, 2022 at 15:40

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Most likely the wire is not just creating a simple DC magnetic field, but alternating at some frequency, and the robot has a sensor tuned to the same frequency. Rejecting other frequencies greatly reduces the amount of noise in the measurement. You should have no problem detecting an AC magnetic field with a certain frequency from a short distance away.

If your system needs more than one navigation beacon, you might choose to use a different frequency for each, or turn it on and off in a repeating binary pattern, so the robot can detect which beacon it's close to.

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