(a) Aircraft sometimes acquire small static charges. Suppose a supersonic jet has a 0.500 μC0.500\textrm{ }\mu\textrm{C} charge and flies due west at a speed of 660 m/s over the Earth’s magnetic south pole (near Earth's geographic north pole), where the 8.00×105 T8.00\times 10^{-5}\textrm{ T} magnetic field points straight down. What are the direction and the magnitude of the magnetic force on the plane? (b) Discuss whether the value obtained in part (a) implies this is a significant or negligible effect.
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Final Answer
  1. 2.64×108 N2.64\times 10^{-8}\textrm{ N}
  2. The acceleration this force would cause on a 440,000 kg Boeing 747 aircraft is 6×1014 m/s26\times 10^{-14}\textrm{ m/s}^2. The force is negligible since this acceleration would not be possible to measure.

Solution video

OpenStax College Physics for AP® Courses, Chapter 22, Problem 8 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. An airplane is flying over the South pole where conveniently, the magnetic field lines are straight down and that makes them perpendicular to this plane's velocity, which is straight to the West. And I am taking a view of somebody just sort of floating in the air, looking at this plane flying by and we are looking towards the North so North is away from us and South is towards us, West is to the left and East is to the right. So we are given the charge on the plane, 0.500 microcoulombs, written as 0.500 times 10 to the minus 6 coulombs, the speed is 660 meters per second and Earth's magnetic field here is 8.00 times 10 to the minus 5 tesla. So first question is what is the direction of the force due to the magnetic field on this charged plane that's moving and so we will align our thumb in the direction of velocity to the left, our fingers should be pointing straight down along the magnetic field lines and our palm points in the direction of force on a positive charge and this plane is positively charged and our palm is facing out of the page and out of the page in this drawing is to the South. So the force is to the South and the magnitude is the charge— 0.500 times 10 to the minus 6 coulombs— times the speed of 660 meters per second times the magnetic field strength times sin of the angle between the velocity and the magnetic field but that's a 90 degree angle so sin of that is 1 and we have 2.64 times 10 to the minus 8 newtons and the next question is is that a significant force? So we can imagine how much acceleration it might cause to an airplane and suppose this is a 747 airplane— I looked up on Wikipedia what the mass of a Boeing 747 is and it's 440000 kilograms— so taking that force and divided it by this mass gives an acceleration of 6 times 10 to the minus 14 meters per second squared; that is certainly negligible so this force is negligible.