Question

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)hat(k)`
B. `((pi)/(2) + 1 )a^(2) Ihat(k)`
C. ` - ((pi)/(2) + 1 )a^(2) Ihat(k)`
D. `( 2 pi + 1)a^(2) Ihat(k)`

Answer 1

Correct Answer - B
The magnetic moment of a current carrying loop is given by ` vec(M) = NL vec(A)`
Here ` N = 1 , A = a^(@) + 2 pi ((a)/(2))^(2) = a^(2) [ 1 + (pi)/(2) ]` , the direction is towards positive ` z- axis `.
` vec(M) = Ia^(2) [ 1 + (pi)/(2)] hat (k) `