Shown in Fig. is an end-on view of three long, straight, parallel conductors spaced equal distances a apart. The outer conductors carry current I out of the page, the middle conductor carries current I into the page. Where in the plane of the page is the magnetic field zero?

Explanation

For magnetic field to be zero at P,

`vecB_P=0, 2B_1 cos theta=B_2`
`2(mu_0I)/(2pi(sqrt(a^2+y^2))) y/(sqrt(a^2+y^2))= (mu_0I)/(2piy)`
`implies y=+-a`