(a) What is the force per meter on a lightning bolt at the equator that carries 20,000 A perpendicular to the Earth’s 3.00×105 T3.00\times 10^{-5}\textrm{ T} field? (b) What is the direction of the force if the current is straight up and the Earth’s field direction is due north, parallel to the ground?
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Final Answer
  1. 0.600 N/m0.600\textrm{ N/m}
  2. West

Solution video

OpenStax College Physics for AP® Courses, Chapter 22, Problem 34 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We want to know what is the force per meter due to Earth's magnetic field on this column of ionized air due to this lightning bolt that carries 20000 amps and the magnetic field strength is 3.00 times 10 to the minus 5 tesla and the magnetic field and the lightning bolt direction are perpendicular. So force on a current carrying wire so to speak— the wire in this case being this column of air that's been ionized— equals the current times the length of the air times magnetic field strength multiplied by sin Θ. We are not given the length of the air but we can find the force per length by dividing both sides by l and so F over l then is IBsin Θ. So that's 20000 amps times 3.00 times 10 to the minus 5 tesla times sin of 90, which is 1, and that is 0.600 newtons per meter. Now what if the current is straight up, which in this top-down picture looking from the clouds towards the ground, we would have this current represented as a dot coming towards us and the magnetic field is North and the force then if you use your right hand pointing your fingers in the direction of the magnetic field and your thumb pointing in the direction of current coming out of the page your palm pushes to the left, the force would be to the left and that is in the West direction.