A wire carrying a 10A current is bent to pass through various sides of a cube of side 10 cm as shown in fig. A magnetic field `vecB=(2hati-3hatj+hatk)T` is present in the region.

Find the net torque on the loop.

Options

A. `-0.1hati+0.4hatkNm`
B. `-0.1hati-0.4hatkNm`
C. `0.2hati-0.4hatkNm`
D. `0.1hati-0.4hatkNm`

Answer

c

Explanation

The net force on a current carrying loop of any arbitrary
shope in a uniform magnetic field is zero.
`vecF_(n et)=0`
The given loop can be considered to be a superposition of three
loops as shown in Fig. The area vector of the three loops
(1) ,(2) and (3) are

`vecA_1=(1/2xx10xx10xx10^-4)hatjm^2`
`vecA_2=(1/2xx10xx10xx10^-4)hatk m^2`
`vecA_3=(1/2xx10xx10xx10^-4)hati m^2`
Magnetic moment vector,
`vecmu=ivecA=10(0.01hati+0.005hatj+0.005hatk)Am^2`
`=(0.1hati+0.05hatj+0.05hatk)Am^2`
Torque,
`vectau=(0.1hati+0.05hatj+0.05hatk)xx(2hati-3hatj+hatk)`
`|[hati ,hatj ,hatk],[0.1, 0.05, 0.05],[2 ,-3 ,1]| =0.2hati-0.4hatkNm`