A rectangular loop consists of `N = 100` closed wrapped turns and has dimensions `(0.4 m xx 0.3 m)`. The loop is hinged along the y-axis and its plane makes an angle `theta = 30^@` with the x-axis. What is the magnitude of the torque exerted on the loop by a uniform magnetic field `B = 0.8 T` directed along the x-axis when current is `i = 1.2 A` in the direction shown. What is the expected direction of rotation of the loop?

Answer

A, B, C, D

Explanation

`M=Ni(OAxxAB)`
`=Ni(OAxxOC)`
`=(100)(1.2)[(0.4hatj)xx(0.03cos30^@hati+0.3sin30^@hatk)]`
`=(7.2hati-12.47hatk)A-m^2`
`tau=MxxB`
`=[(7.2hati-12.47hatk)xx(0.8hati)]`
`=(-9.98hatj)N-m`
`:. |tau|=9.98N-m`
Torque vector and expected direction of rotation is shown in figure.