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 54.8 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 36.6 mA current, starting from the lower south corner of the window, and ending at the opposite corner, which is 1.53 m to the north and 0.850 m upward. The sign spells out the word "DONUTS" 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.) Remember, the shape of the sign is irrelevant-all that matters are the positions of the endpoints and the magnitude of the current. Can you write a vector, in terms of components, for the length of the current-carrying neon tube from the starting point to the ending point? Can you write a vector in terms of components for the magnetic field? What is the expression for the vector magnetic force, and how do you evaluate a cross product? Note the defined directions and be careful of signs and units. uN
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 54.8 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 36.6 mA current, starting from the lower south corner of the window, and ending at the opposite corner, which is 1.53 m to the north and 0.850 m upward. The sign spells out the word "DONUTS" 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.) Remember, the shape of the sign is irrelevant-all that matters are the positions of the endpoints and the magnitude of the current. Can you write a vector, in terms of components, for the length of the current-carrying neon tube from the starting point to the ending point? Can you write a vector in terms of components for the magnetic field? What is the expression for the vector magnetic force, and how do you evaluate a cross product? Note the defined directions and be careful of signs and units. uN
Chapter11: Magnetic Forces And Fields
Section: Chapter Questions
Problem 108CP: A wire ismade into a circular shape of radius R and pivoted along a central support.The two ends of...
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Transcribed Image Text: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 54.8 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 36.6 mA current, starting from the lower south corner of the window, and
ending at the opposite corner, which is 1.53 m to the north and 0.850 m upward. The sign spells out the word "DONUTS" 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.)
В
Remember, the shape of the sign is irrelevant-all that matters are the positions of the endpoints and the magnitude of the current. Can you write a vector, in terms of
components, for the length of the current-carrying neon tube from the starting point to the ending point? Can you write a vector in terms of components for the
magnetic field? What is the expression for the vector magnetic force, and how do you evaluate a cross product? Note the defined directions and be careful of signs and
units. µN
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