A circular ring with area 4.45 cm? is carrying a current of 13.5 A. The ring, initially at rest, is immersed in a region of uniform magnetic field given by B = (1.35 x 10-2 T)(12î +33 – 4Ê). The ring is positioned initially such that its magnetic moment orientation is given by i, = µ(-0.8î + 0.6j), where u is the (positive) magnitude of the magnetic moment. (a) Find the initial magnetic torque on the ring. (b) The ring (which is free to rotate around one diameter) is released and turns through an angle of 90.0° , at which point its magnetic moment orientation is given by i, =-µk. Determine the decrease in potential energy. (c) If the moment of inertia of the ring about a diameter is 2.50 x 10-7 kg m² , determine the angular speed of the ring as it passes through the second position.

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Review I Constants
Enter your answer with a different unit type. Review a list of acceptable units.
A circular ring with area 4.45 cm² is carrying a current of 13.5 A.
The ring, initially at rest, is immersed in a region of uniform
magnetic field given by
B = (1.35 x 10-2 T)(12i +3j – 4k). The ring is positioned
initially such that its magnetic moment orientation is given by
ji; = µ(-0.8i + 0.6j), where µ is the (positive) magnitude of
the magnetic moment.
As expected for the object starting from the rest, the kinetic energy is equal to the change in potential energy with opposite sign.
Part E
(a) Find the initial magnetic torque on the ring.
Find the ring's angular speed when it is in the second orientation.
(b) The ring (which is free to rotate around one diameter) is
released and turns through an angle of 90.0° , at which point its
Express your answer in radians per second.
• View Available Hint(s)
magnetic moment orientation is given by f = -µk. Determine
the decrease in potential energy.
W = 87.5 rad/s
(c) If the moment of inertia of the ring about a diameter
is 2.50 x 10-? kg · m² , determine the angular speed of the ring
as it passes through the second position.
Submit
Previous Answers
Correct
Correct answer is shown. Your answer 87.49 rad/s was either rounded differently or used a different number of significant figures than required for
this part.
The ring rotates rather fast because of the small moment of inertia.
EVALUATE
Part F
If the ring were free to rotate around any diameter, in what direction would the magnetic moment point when the ring is in a state of stable equilibrium? Enter
the unit vector of that direction of the magnetic moment.
Express your answer in terms of the unit vectors i, j, and k.
View Available Hint(s)
?
Submit
1|ミ
Transcribed Image Text:Review I Constants Enter your answer with a different unit type. Review a list of acceptable units. A circular ring with area 4.45 cm² is carrying a current of 13.5 A. The ring, initially at rest, is immersed in a region of uniform magnetic field given by B = (1.35 x 10-2 T)(12i +3j – 4k). The ring is positioned initially such that its magnetic moment orientation is given by ji; = µ(-0.8i + 0.6j), where µ is the (positive) magnitude of the magnetic moment. As expected for the object starting from the rest, the kinetic energy is equal to the change in potential energy with opposite sign. Part E (a) Find the initial magnetic torque on the ring. Find the ring's angular speed when it is in the second orientation. (b) The ring (which is free to rotate around one diameter) is released and turns through an angle of 90.0° , at which point its Express your answer in radians per second. • View Available Hint(s) magnetic moment orientation is given by f = -µk. Determine the decrease in potential energy. W = 87.5 rad/s (c) If the moment of inertia of the ring about a diameter is 2.50 x 10-? kg · m² , determine the angular speed of the ring as it passes through the second position. Submit Previous Answers Correct Correct answer is shown. Your answer 87.49 rad/s was either rounded differently or used a different number of significant figures than required for this part. The ring rotates rather fast because of the small moment of inertia. EVALUATE Part F If the ring were free to rotate around any diameter, in what direction would the magnetic moment point when the ring is in a state of stable equilibrium? Enter the unit vector of that direction of the magnetic moment. Express your answer in terms of the unit vectors i, j, and k. View Available Hint(s) ? Submit 1|ミ
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