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

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Magnetic moment of a current carrying loop M = N I A Here N = 1 , A = a 2 + 2 π ( 2 a ​ ) 2 = a 2 [ 1 + 2 π ​ ] From Screw law, direction of m is outward or in +ve z-direction. ∴ M = I a 2 [ 1 + 2 π ​ ] k ^

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