How far from the starter cable of a car, carrying 150 A, must you be to experience a field less than the Earth’s (5.00×105 T5.00\times 10^{-5}\textrm{ T})? Assume a long straight wire carries the current. (In practice, the body of your car shields the dashboard compass.)
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Final Answer

0.600 m0.600\textrm{ m}

Solution video

OpenStax College Physics, Chapter 22, Problem 66 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. A starter cable of a car carries a high current of 150 amps and it produces a magnetic field and the question is how far from the wire do you need to be such that the field produced by that wire has a strength less than that of the Earth? So the magnetic field from a long, straight current carrying wire is permeability of free space multiplied by the current divided by 2π times the distance from the wire. So we can solve for r by multiplying both sides by r divided by B and we have the distance then is μ naughtI over 2πB. So this is the distance at which the field will equal the field strength from the Earth so beyond this the field due to the wire will be less than that of the Earth. So that's 4π times 10 to the minus 7 tesla meters per amp times 150 amps divided by 2π times 5.00 times 10 to the minus 5 tesla and that's 0.600 meters away from the wire.