Calculate the size of the magnetic field 20 m below a high voltage power line. The line carries 450 MW at a voltage of 300,000 V.
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Final Answer

1.50×105 T1.50\times 10^{-5}\textrm{ T}

Solution video

OpenStax College Physics, Chapter 22, Problem 72 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. These power lines are a long straight wire and so we have a formula for finding the magnetic field due to that: it's μ naught times the current in the wire divided by 2π times the distance from the wire r but we are not given the current, we are given instead the voltage in these power lines and the total power that they deliver. And so we need to know that power is current multiplied by voltage and we can solve for current by dividing both sides by V and so current is power divided by voltage. So we substitute P over V in place of I and the magnetic field then is μ naught times P over 2πr times V. So that's 4π times 10 to the minus 7 tesla meters per amp times 450 times 10 to the 6 watts divided by 2π times 20.0 meters times 300000 volts and that's 1.50 times 10 to the minus 5 tesla.