A current `I=IA` flowing through an infinite long wire `A_1` divides between two infinite long wires `A_2` and `A_3` at junction B. The magnitude of the magnetic field at point O due to current through wires is :

Answer

Zero

Explanation

Let Mag. field at O due to current through wires
`A_1, A_2, A_3` be `vecB_1, vec_2` and `vecB_3` respectively. Then
`vecB_1=0, :'`O` lies on the axis of wire `A_1`
`B_2=(mu_0)/(4pi)(I)/((1//2))[sin 90^@+sin0^@](-hatk)`
`=10^-7xx1xx2[1+0](-hatk)=-2xx10^-7hatk`
`vecB_3=(mu_0)/(4pi)(I)/((1//2))[sin 90^@+sin 90^@]hatk`
`=10^-7xx1xx2[0+1]hatk=2xx10^-7hatk`
`:.` Total magnetic field at O is
`vecB=vecB_1+vecB_2+vecB_3`
`=0+(-2+10^-7hatk)+(2xx10^-7hatk)=0`