Two long wires PQR and MNP carry equal current I as shown such that QR and NP are parallel. Find the magnetic field at origin O.

Due to PQ and MN, magnetic field at O will be zero.r=a  sin 600 = 32  aBQR=μ04π Ir   sin 900 −  sin 300 ⊗= μ04π  I3 a/2 ×  12  ⊗  = μ0I4π3 a ⊗BNP =   μ04π Ir  sin 900 +  sin 300 ⊙ = 3μ0I4π3a⊙Net field at O,B=BNP−BQR  =  μ0I23πa ⊙