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MasteringPhysics: Assign... x a https://session.masteringphysics.com/myct/itemview?assignmentproblemID 46273736 University of Michigan Physics 235 Winter 2015 Exercise 27.42 Exercise 27.42 The plane of a rectangular loop of wire with a width of 5.0cm and a height of 8.0cm is parallel to a magnetic field of magnitude 0.20T.The loop carries a current of 6.2A Google Part A What torque acts on the loop? Express your answer using two significant figures. Submit My Answers Give Up Part B What is the magnetic moment of the loop? Express your answer using two significant figures My Answers Give Up Part C What is the maximum torque that can be obtained with the same total length of wire carrying the same current in this magnetic field? Express your answer using two significant figures. My Answers Give Up Signed in as Tony Bryant Help close Resources r previous I 3 of 14 I next Continue Provide Feedback 11:08 AM 2/18/2015

Explanation / Answer

B.
Magnetic moment, mu = IA
mu = 6.2 * (0.05 x 0.08) = 0.0248 Am2

A.
Torque = mu x B
Since mu is perpendicular to B, hence
Torque = mu B = 0.0248 x 0.2 = 0.00496 Nm

C.
The maximum torque would be achieved for the loop with the largest area for the available length of wire. The shape of the optimum loop is a circle. If the sides are a and b, then the radius r of the circle satis?es
2pir = 2(a + b)
r = (a + b)/pi = (0.05 + 0.08) / pi
r = 0.0414
Maximum Torque = pir2IB = 3.14 * (0.0414)^2 * 6.2 * 0.2
Maximum Torque = 6.674 x 10-3 Nm

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