Two identical long parallel wires carry current ' I₁ ' and ' I₂ ' such that I₁ > I₂ . When the currents are in the same direction, the magnetic field at a point midway between the wires is 6 10⁻⁶ T . If the direction of ' I₂ ' is reversed, the field becomes 3 10⁻⁵ T . The ratio ( I₁ I₂ ) is

Step-by-step solution

Let the distance between the two parallel wires be 2d . The distance of the midway point from each wire is d . The magnetic field due to a long straight wire carrying current I at a distance d is given by B = ₀ I 2 d . When the currents I₁ and I₂ are in the same direction, the magnetic fields at the midway point are in opposite directions. Since I₁ > I₂ , the net magnetic field is: B₁ = ₀ 2 d (I₁ - I₂) = 6 10⁻⁶ T When the direction of I₂ is reversed, the currents are in opposite directions, so their magnetic fields