An arbitrarily curved wire that carries a current between two endpoints in the presence of a uniform magnetic field will experience the same net magnetic force as a straight wire carrying the same current between the same endpoints. Essentially, any forces experienced by parts of the wire that curve or twist away from the straight-line path are canceled out by forces on sections that curve back toward the original path. Furthermore, if the wire forms a closed loop in between the endpoints, the net force on the closed loop is zero. Using this result, consider a town where the Earth's magnetic field has a magnitude of 53.3 µT. The magnetic field vector lies in a vertical plane defined by the north-south and up-down axes, and it points 60.0° below the northward direction. In this town, a storefront window lies along the north-south vertical plane, and in the window is a neon sign (which is a thin current-carrying discharge tube). The sign carries a 35.4 mA current, starting from the lower south corner of the window, and ending at the opposite corner, which is 1.39 m to the north and 0.850 m upward. The sign spells out the word "OPEN" between the two points. What is the net vector magnetic force (in µN) on the neon sign? (Take east to be the +x-axis, up to be the +y-axis, and south to be the +z-axis. Do not include units in your answer.)

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter31: Gauss’s Law For Magnetism And Ampère’s Law

Section: Chapter Questions

Problem 72PQ

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An arbitrarily curved wire that carries a current between two endpoints in the presence of a uniform magnetic field will experience the same net magnetic force as a straight wire carrying the same current between the same endpoints. Essentially, any forces experienced by parts of the wire that curve or twist away from the straight-line path are canceled out by forces on sections that curve back toward the original path. Furthermore, if the wire forms a closed loop in between the endpoints, the net force on the closed loop is zero.

Using this result, consider a town where the Earth's magnetic field has a magnitude of 53.3 µT. The magnetic field vector lies in a vertical plane defined by the north-south and up-down axes, and it points 60.0° below the northward direction. In this town, a storefront window lies along the north-south vertical plane, and in the window is a neon sign (which is a thin current-carrying discharge tube). The sign carries a 35.4 mA current, starting from the lower south corner of the window, and ending at the opposite corner, which is 1.39 m to the north and 0.850 m upward. The sign spells out the word "OPEN" between the two points. What is the net vector magnetic force (in µN) on the neon sign? (Take east to be the +x-axis, up to be the +y-axis, and south to be the +z-axis. Do not include units in your answer.)

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