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

Answer

D

Explanation

`vec(mu) = Ivec(A) = I[(pia^(2))/(2) xx 4 + a^(2)]hat(k)`
`= (2pi + a) I a^(2) hat(k)`