Two long straight parallel wires are placed in a three-dimensional coordinate system. The first wire lies along the z -axis and carries a current I in the +z direction. The second wire is parallel to the z -axis, passes through the point (a, 0, 0) , and carries a current 2I in the +z direction. The magnitude of the net magnetic field at a point P located at (0, a, 0) is given by ₀ I 2 a X . The value of X is

Step-by-step solution

The magnetic field due to a long straight wire is given by B = ₀ I 2 r ( l r ) , where l is the direction of current and r is the position vector from the wire to the point. For the first wire (along z -axis): Current direction l ₁ = k Position vector of P(0, a, 0) from the origin is r ₁ = a j B ₁ = ₀ I 2 a ( k j ) = ₀ I 2 a (- i ) For the second wire (passing through (a, 0, 0) ): Current direction l ₂ = k Position vector of P(0, a, 0) from (a, 0, 0) is r ₂ = (0 - a) i + (a - 0) j = -a i + a j Distance r₂ = | r ₂|