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^2Ihatk`
B. `(pi/2+1)a^2Ihatk`
C. `-(pi/2+1)a^2Ihatk`
D. `(2pi+1)a^2Ihatk`

Answer

B

Explanation

Area enclosed by the given current loop is
A=Area of 4 semisphere each of radius `(a//2)` plus are of a square of each side a
`=1/2[4pi(a//2)^2]+a^2=(pia^2)/(2)+a^2=(pi/2+1)a^2`
Area vector, `vecA=(pi/2+1)a^2hatk`
Magnetic moment of the current loop,
`vecM=IvecA=I(pi/2+1)a^2hatk=(pi/2+1)a^2Ihatk`