A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and b, then the magnitude and direction of magnetic moment of the loop ABCDEFA is:

Options

A. `sqrt(2)` abl,along ` ((hat(j))/(sqrt(5))+(2hat(k))/(sqrt(5)))`
B. abl,along `((hat(j))/(sqrt(5)) +(2hat(k))/(sqrt(5)))`
C. `sqrt(2)` abl,along `((hat(j))/(sqrt(2)) + (hat(k))/(sqrt(2)))`
D. abl, along `((hat(j))/(sqrt(2))+(sqrt(k))/(sqrt(2)))`

Answer

C

Explanation

LOOP = ABCD
`vec(M)_(1) = (abI)(hat(j)+hat(k))`
Loop DEFA
`vec(M)_(2) = (abI) hat(j)`
` vec(M) = vec(M)_(1)+vec(M)_(2) = abI (hat(j)+hat(k))`
` |vec(M)| = sqrt(2)` abI
direction = along ` ((hat(j))/(sqrt(2))+(hat(k))/(sqrt(2)))`