In the given loop length of each side is `a`. Current flowing through the loop is `I=1` amp. Find its manetic dipole moment.

Options

A. `(a^(2))/(sqrt(2))(hat(j))+(a^(2)(1-sqrt(2)))/(sqrt(2))(hat(i))-a^(2)(hat(k))`
B. `(a^(2))/(sqrt(2))(-hat(i))+(a^(2)(1-sqrt(2)))/(sqrt(2))(hat(j))+a^(2)(-hat(k))`
C. `-a^(2)(hat(i))-(a^(2)(1-sqrt(2)))/(sqrt(2))(hat(j))-(a^(2))/(sqrt(2))-(a^(2))/(sqrt(2))(hat(k))`
D. none of these

Answer

B

Explanation

`tau=Ia^(2)(-hat(k))+Ia^(2)(-hat(j))+Ia^(2)cos 45^(@)(-hat(j))+Ia^(2)sin 45^(@)(hat(j))`
`=(Ia^(2))/(sqrt(2))(-hat(i))+((Ia^(2))/(sqrt(2))-Ia^(2))hat(j)+Ia^(2)(-hat(k))`
`=(a^(2))/(sqrt(2))(-hat(i))+(a^(2)(1-sqrt(2)))/(sqrt(2))(hat(j))+a^(2)(-hat(k))`.