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(b) The torque exerted by the field on the dipole is given by the following cross product. 7-pxi Submit - -12.6 -10 +11.7 ×108 N-m) Skip (you cannot come back) 10-12 cm (7.8 x +4.9 i) x 10³ N/C]

(b) The torque exerted by the field on the dipole is given by the following cross product. 7-pxi Submit - -12.6 -10 +11.7 ×108 N-m) Skip (you cannot come back) 10-12 cm (7.8 x +4.9 i) x 10³ N/C]

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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I need help with prt 5, thanks

Tutorial Exercise A small, rigid object carries positive and negative 4.50-nC charges. It is oriented so that the positive charge has coordinates (-1.20 mm, 1.30 mm) and the negative charge is at the point (1.60 mm, -1.30 mm). (a) Find the electric dipole moment of the object. The object is placed in an electric field E= (7.80 x 10³1 - 4.90 x 10³) N/C. (b) Find the torque acting on the object. (c) Find the potential energy of the object-field system when the object is in this orientation. (d) Assuming the orientation of the object can change, find the difference between the maximum and the minimum potential energies of the system. Part 1 of 8 - Conceptualize An electric dipole in an external electric field behaves like a needle mounted at its midpoint on a vertical pivot. The dipole can be forced to another orientation by exerting a torque on it to move it from its position of lowest energy. When released, it will oscillate like a torsional pendulum. The electric dipole in this problem is small in size like one that might be used in a classroom experiment. The dipole moment will be in the picocoulomb-meter range and the torque, which tends to turn it clockwise to align it with the field, will be on the order of a few nanonewton-meters, with the potential energy on the order of nanojoules. In the orientation described, the dipole is close to its maximum potential energy since its moment is close to being opposite the field direction. Part 2 of 8 - Categorize We use the definition of dipole moment and the equation for torque exerted on a dipole by an electric field. We compute the dot product of the moment and the electric field vectors to find the potential energy and compute the maximum potential energy for the dipole when its moment is opposite in direction to the electric field. Part 3 of 8 - Analyze (a) The displacement in vector notation from negative to positive charge along the dipole is given by the following. -1.2 + 1.30 1.3 j) mm - 1.6✔ 1.6 î+ -1.3 ĵ) mm 2a = -1.2✔ = -2.8✔✔✔ -2.8 +2.6 2.6 1x 10-³ m
Transcribed Image Text:Tutorial Exercise A small, rigid object carries positive and negative 4.50-nC charges. It is oriented so that the positive charge has coordinates (-1.20 mm, 1.30 mm) and the negative charge is at the point (1.60 mm, -1.30 mm). (a) Find the electric dipole moment of the object. The object is placed in an electric field E= (7.80 x 10³1 - 4.90 x 10³) N/C. (b) Find the torque acting on the object. (c) Find the potential energy of the object-field system when the object is in this orientation. (d) Assuming the orientation of the object can change, find the difference between the maximum and the minimum potential energies of the system. Part 1 of 8 - Conceptualize An electric dipole in an external electric field behaves like a needle mounted at its midpoint on a vertical pivot. The dipole can be forced to another orientation by exerting a torque on it to move it from its position of lowest energy. When released, it will oscillate like a torsional pendulum. The electric dipole in this problem is small in size like one that might be used in a classroom experiment. The dipole moment will be in the picocoulomb-meter range and the torque, which tends to turn it clockwise to align it with the field, will be on the order of a few nanonewton-meters, with the potential energy on the order of nanojoules. In the orientation described, the dipole is close to its maximum potential energy since its moment is close to being opposite the field direction. Part 2 of 8 - Categorize We use the definition of dipole moment and the equation for torque exerted on a dipole by an electric field. We compute the dot product of the moment and the electric field vectors to find the potential energy and compute the maximum potential energy for the dipole when its moment is opposite in direction to the electric field. Part 3 of 8 - Analyze (a) The displacement in vector notation from negative to positive charge along the dipole is given by the following. -1.2 + 1.30 1.3 j) mm - 1.6✔ 1.6 î+ -1.3 ĵ) mm 2a = -1.2✔ = -2.8✔✔✔ -2.8 +2.6 2.6 1x 10-³ m
Part 4 of 8 - Analyze The electric dipole moment is given by p P = 2aq = Submit = -2.8 = -12.6 -2.8 Î+2.6 -12.6 -12.6 + 11.7 Î + 11.7 Part 5 of 8 - Analyze (b) The torque exerted by the field on the dipole is given by the following cross product. 7 = P x E Р x 10-8 N-m Skip (you cannot come back) 2.6 1) × 10-3 m m)k 11.7 x 10-¹2 C. m. 4.5✔ × 10-¹² C-m] x [( 7.8 4.5 x 10-⁹ c) Î + -4.9 ₁) × 10³ N/C] x
Transcribed Image Text:Part 4 of 8 - Analyze The electric dipole moment is given by p P = 2aq = Submit = -2.8 = -12.6 -2.8 Î+2.6 -12.6 -12.6 + 11.7 Î + 11.7 Part 5 of 8 - Analyze (b) The torque exerted by the field on the dipole is given by the following cross product. 7 = P x E Р x 10-8 N-m Skip (you cannot come back) 2.6 1) × 10-3 m m)k 11.7 x 10-¹2 C. m. 4.5✔ × 10-¹² C-m] x [( 7.8 4.5 x 10-⁹ c) Î + -4.9 ₁) × 10³ N/C] x
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