A rectangular coil consists of N = 130 closely wrapped turns and has dimensions

Question

A rectangular coil consists of N = 130 closely wrapped turns and has dimensions a = 0.400 m and b = 0.300 m The coil is hinged along the y axis, and its plane makes an angle theta = 30.0 degree with the x axis (see figure below). (a) What is the magnitude of the torque exerted on the coil by a uniform magnetic field B = 0.045 T directed in the positive x direction when the current is I = 1.20 in the direction shown? (b) If you are looking downward from the positive y direction, what is the expected direction of rotation of the coil? clockwise counterclockwise

Explanation / Answer

Here ,

N = 130

area of the loop , A = a * b

A = 0.4 * 0.3 = 0.12 m^2

A = 0.12 m^2

magnetic moment , u = N*I*A

u = 0.12 * 1.2 * 130

u = 18.72 A.m^2

torque acting on the loop = u * B * cos(30)

torque acting on the loop = 18.72 * 0.450 * cos(30)

torque acting on the loop = 7.295 N.m

the torque acting on the loop is 7.295 N.m

b)

as looking downwards from the positive y direction

the direction of rotation is counterclockwise

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