Two infinitely long wires are placed at (1 ~cm , 1 ~cm ) and (+1 ~cm ,-1 ~cm ) with 1 ~A current in each and in the same directions perpendicular to x y -plane. let the magnetic field due to these current carrying wires at the origin be B . If B₀ is the magnitude of the field if only one of them was present. then | B | B₀ is

Step-by-step solution

The given situation is shown below Wires are located at position A and B aligned O A & =O B= 1^2+1^2 = 2 ~cm & = 2 10⁻² ~m aligned Magnitude of net magnetic field due to both wire having current 1 ~A is given as aligned | B | & = [ ₀ I 2 (O A) ]^2+ [ ₀ I 2 (O B) ]^2 & = ( ₀ 1 2 2 )^2+ ( ₀ 1 2 2 )^2 = ₀ 2 2 2 = ₀ 2 & | B |= ₀ 2 aligned Magnitude of magnetic field due to individual wire O A , aligned & B₀= ₀ I 2 (O A) = ₀ I 2 2 = ₀ 2 2 & | B | B₀ = ₀ / 2 ₀ / 2 2 = 2 aligned