An infinitely long wiré carrying 1 A current in the +z direction is placed at (1 ~cm , 1 ~cm ) . Another wire carrying 1 ~A in +x direction is placed at y=1 ~cm . If the magnetic field due to this configuration at the origin is B . Let B₀ be the magnitude of the field if only the wire at (1 ~cm , 1 ~cm ) was present, then B B₀ is

Step-by-step solution

Given arrangement is shown below Distance of conductor I from origin, is aligned & d= x^2+y^2 = 1+1 & d= 2 ~cm = 2 10⁻² ~m aligned Magnetic field due to wire Iat origin is B₁= ₀ I₁ 2 d or B₁=B₀= ₀ 2 d [ I₁=I₂=1 ~A ] Now, in vector form, B ₁= ₀ 2 d ( 1 2 i - 1 2 j ) = ₀ 2 2 10⁻² ( 1 2 i - 1 2 j ) And field of conductor II is aligned B ₂ & = ₀ I₂ 2 y (- k ) & = ₀ 2 10⁻² (- k ) [ y=1 ~cm =1 10⁻² ~m ] aligned Hence, magnetic field due to both conductors, aligned & B = B ₁+ B ₂ & = ₀ 2 ( 1 2 i - 1 2 j ) 1 2 10⁻² + ₀ 2 (