Question

A square loop of side l carries a current i. it is placed as shown in figure. Find the magnetic moment of the loop.

Answer 1

Magnetic moment `vec(M) = ivec(A)`
`vec(A) = vec(AB) xx vec(BC)`
`vec(AB) = l cos 30^(@) hat(i) + l sin 30^(@)k`
`vec(BC) = -l hat(j)`
`vec(A) = (l cos 30^(@) hat(i) + l sin 30^(@)k) xx (-l hat(j))`
`= -l^(2) (sqrt3)/(2) hat(k) + (l^(2))/(2) hat(i)`
So magnetic moment `vec(M) = ivec(A)`
`= (il^(2))/(2) [hat(i) - sqrt3 hat(k)]`