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A loop carrying current I lies in the x...

A loop carrying current `I` lies in the ` x-y ` plane as shown in the figure . The unit vector ` hat k` is coming out of the plane of the paper . The magnetic moment of the current loop is

A

`a^(2)Ik`

B

`((pi)/2+1)a^(2)IK`

C

`-((pi)/2+1)a^(2)IK`

D

`(2pi+1)a^(2)IK`

Text Solution

Verified by Experts

The correct Answer is:
B
Area of the given loop is A= (area of two circles of radius `a/2` and area of square of side a)
`=2pi(a/2)^(2)+a^(2)=((pi)/2+1)a^(2)|M|=IA=((pi)/2+1)A^(2)I`
From screw law direction of M is outwards or in positive z- direction `:.M=((pi)/2+1)a^(2)Ihatk`
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