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 :

Options

A. zero
B. `2xx10^-7T`
C. `4xx10^-7T`
D. `8xx10^-7T`

Answer

A

Explanation

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