In Fig. Find the magnetic field at common centre.

Explanation

Consider Fig.
`vecB_P=(vecB_1)_P+(vecB_2)_P+(vecB_3)_P+(vecB_4)_P+(vecB_5)_P`
where `(vecB_1)_P=(mu_0i)/(4pi((3a)/2))(-hatj)` (semi-infinite wire)

`(vecB_2)_P=(mu_0i)/(4pi((3a)/2))(-hatk)`
`(vecB_3)_P=0`
`(vecB_4)_P=(mu_0i)/(4(a/2))(-hatk) implies (vecB_5)_P=(mu_0i)/(4pi(a/2))(-hatj)`
`(vecB)_P=(mu_0i)/(2a)[-(1/(3pi)+1/pi)hatj-(1-1/3)hatk]`
`vecB_P=(mu_0i)/(3a)[2/pi hatj-hatk]`