Two semi infinitely long straight current carrying conductors are held in the form as shown in figure. One common end of them is at the origin. If both the conductors carry same current I, find the value of the magnetic field induction at a point (a, b).

Explanation

For the conductor along the X-axis the magnetic field
`B_(1) = (mu_(0)I)/(4 pi b) [sin theta_(2) + sin pi//2]` along the negative z-axis
`= (mu_(0) I)/(4 pi b) [1 + (a)/(sqrt(a^(2) + b^(2)))]`
For the conductor along y-axis the magnetic field is
`B_(2) = (mu_(0)I)/(4pi a) [1 + (b)/(sqrt(a^(1) + b^(2)))]` along the negative z-axis
The net magnetic field is
`vec(B) = vec(B_(1)) + vec(B_(2))`
`= (mu_(0) I)/(4 pi) [((1)/(a) + (1)/(b)) + (1)/(sqrt(a^(2) + b^(2))) ((a)/(b) + (b)/(a))] = (mu_(0)I)/(4 pi) [((a + b))/(ab) + (sqrt(a^(2) + b^(2)))/(ab)]`
`(mu_(0) i)/(4 pi ab) [(a + b) + sqrt(a^(2) + b^(2))]`