1. A rectangular coil consists of N = 95 closely wrapped turns with the dimensio

Question

1. A rectangular coil consists of N = 95 closely wrapped turns with the dimensions as shown. The coil is hinged along the y-axis, and its plane of makes an angle theta = 30 degree with the x-axis. (a) What is the magnitude of torque exerted on the coil by a uniform magnetic field B = 0.750 T directed in the positive x direction when the current is I = 1.20 A in the direction shown? (b) What is the expected direction of the rotation of the coil if you were looking from above? ANS = 8.89 N . m, CW

Explanation / Answer

SOLUTION =

Torque = magnetic moment X magnetic field (*where X = cross product)

Torque = magnetic moment * magnetic field * sin(phi)

where,

magnetic moment of coil = N*I*A (*where N =number of closely wrapped turns, I=current, A=area)

we are given the following values in the question:

N = 95

a = 0.400 m and b = 0.300 m

Area = a*b = 0.4m * 0.3m = 0.12 m^2

B = 0.750 T

I = 1.20 A

theta = 30 degrees

phi = 60 degrees (* it is the angle between the magnetic moment and the magnetic field 90-30 = 60 )

so the magnetic moment = N*I*A

magnetic moment = (95) * (1.2 A) * (0.12 m^2)

Furthermore plugging this back into the formula for torque we get:

Torque = magnetic moment * magnetic field * sin(theta)

Torque = ((95) * (1.2 A) * (0.12 m^2)) * ( 0.750 T) * sin(60)

Torque = 8.88 N*m

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