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A uniform magnetic field vec(B) = 3 hat ...

A uniform magnetic field `vec(B) = 3 hat i + 4 hat j + hat k` exists in region of space. A semicircular wire of radius of 1 m carrying current 1 A having its centre at (2, 2, 0) is placed in x-y plane as shown in Fig. The force on semicircular wire will be

A

`sqrt2(hati+hatj+hatk)`

B

`sqrt2(hati-hatj+hatk)`

C

`sqrt2(hati+hatj-hatk)`

D

sqrt2(-hati+hatj+hatk)

Text Solution

Verified by Experts

The correct Answer is:
B
Force on semi-circular wire will be same as the force on straight wire `AC`

`vecl=AvecC=2R(cos45^(@)hati+sin45^(@)hatj)=sqrt2(hati+hatj)`
`vecF=IveclxxvecB=1xxsqrt2(hati+hatj)xx(3hati+4hatj+hatk)`
`sqrt2[hati-hatj+hatk]`
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