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

Options

A. `a^(2)Ik`
B. `((pi)/2+1)a^(2)IK`
C. `-((pi)/2+1)a^(2)IK`
D. `(2pi+1)a^(2)IK`

Answer

B

Explanation

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`