A single circular loop of radius r = 1.60 cm carrying a current 1-0.850 A is rot

Question

A single circular loop of radius r = 1.60 cm carrying a current 1-0.850 A is rotating at a constant angular speed = 12.6 rad/s while immersed in a uniform magnetic field of magnitude B = 2.30 T, as shown in the figure. For this problem, you can ignore the effect of gravity (a) What is the maximum torque that acts on the coil? Nm (b) At a particular instant while the coil is rotating, the torque acting on the loop is one fifth of the maximum torque. What is the magnitude of the angle between the magnetic field and the plane of the loop at that instant? (c) What is the magnitude of the maximum change in potential energy of this system as the loop rotates in the magnetic field? mJ

Explanation / Answer

part A :

maximum torque T = NiAB

T = 1 * 0.85 * 3.14* 0.016^2 * 2.3

T = 1.57 *10^-3 Nm

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as T = NIAB Sin theta

sin theta = 1/5

sin theta = 0.2

theta = 11.53 deg

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partC:
max Change of PE = TW

PE = 1.57*10^-3 (sin 90 - sin11.53)

PE = 1.256 mJ

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part D:

Circumference C = 2pir

C = 2pir = 2*3.14 * 0.016 = 0.10048 m

perimeter of square = 4a = 0.10048

a = 0.10048/4 = 0.02512 m

Torque T = NIAB

T = 1 * 0.85* 0.02512^2* 2.3

T = 1.233*10^-3 Nm

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