Find the magnetic field intensity at the point O in the fugure when current I flows in the loop as shown.

Explanation

`vec B_(O) = vec B_1 + vec B_2 + vec B_2 + vec B_3 + vec B_4`
The magnetic field of at O is the vector sum of the magnetic field at O due to the segment 1,2,3 and 4.
`vec B_2 = vec B_4 = 0` as `bar(dl) vec r` for the elements in the segments 2 and 4.
Hence `vec d B = (mu_0 I)/(4 pi)(vec dl xx vec r) = 0 ` for them.
Now, `d vec B = (mu_0 l)/(4 pia) ((3 pi)/(2)) oplus " and "vec B_3 = (mu_0I)/(4 pi b) (pi/2) oplus`
`rArr vec B_O = (mu_0 l)/(8)[(3)/(a) + (1)/(b)]ox`