A rectangular loop consists of 109 closely wrapped turns and has dimensions 0.40

Question

A rectangular loop consists of 109 closely wrapped turns and has dimensions 0.400 m by 0.300 m. The loop is hinged along the y-axis, and the plane of the coil makes an angle of 30.0° with the x-axis (see figure below) I= 1.2A 0.40 m -x 30.0 0.30 m What is the magnitude of the torque exerted on the loop by a uniform magnetic field of 0.856 T directed along the x-axis when the current in the windings has a value of 1.20 A in the direction shown? N·m What is the expected direction of rotation of the loop? clockwise as viewed from above counterclockwise as viewed from the above The magnitude is zero

Explanation / Answer

magnetic dipole u = N*I*A ( cos60 i - sin60 k)

u = 109*1.2*0.4*0.3*(cos60i - sin60 k)

u = 7.848 i - 13.6 k

magnetic field B = 0.856 i

torque = u X B

torque = (7.848 i - 13.6 k) X 0.856 i

torque = - 13.6*0.856 ( k x i)

torque = -11.64 j Nm

magnitude of torque = 11.64 Nm

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clockwise as viewed from above

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