Two identical long parallel wires carry currents ' I ₁ ' and ' I ₂ ' such that I ₁> I ₂ . When the currents are in the same direction, the magnetic field at a point midway between the wires is 8 10⁻⁶ ~T . If the direction of I ₂ is reversed, the field becomes 3.2 10⁻⁵ ~T . The ratio of I ₂ to I ₁ is

Step-by-step solution

The distance from the midway point between two parallel wires to either wire is r = d 2 . The magnetic field at this point due to each wire is B = ₀ I 2 r , giving B₁ = ₀ I₁ d and B₂ = ₀ I₂ d . When currents flow in the same direction, the magnetic fields oppose. With I₁ > I₂ , the net field is B_ net1 = ₀ d (I₁ - I₂) = 8 10⁻⁶ , T . Reversing I₂ makes the fields additive: B_ net2 = ₀ d (I₁ + I₂) = 3.2 10⁻⁵ , T . Dividing these equations gives I₁ + I₂ I₁ - I₂ = 4 . Solving yields I₁ + I₂ = 4(I₁ - I₂) , which simplif