Two long parallel wires carry currents of 5 A and 12 A in opposite directions. A point P is equidistant from both wires such that the lines joining the point P to the wires are perpendicular to each other. If the magnitude of the net magnetic field at P is 52 T , the distance of point P from each wire is ______ cm .

Step-by-step solution

Let the distance of point P from each wire be d . The magnetic fields produced by the two wires at P are mutually perpendicular because the lines joining P to the wires are perpendicular to each other. The magnetic field due to the first wire is B₁ = ₀ I₁ 2 d The magnetic field due to the second wire is B₂ = ₀ I₂ 2 d The net magnetic field is given by vector addition: B_ net = B₁^2 + B₂^2 = ₀ 2 d I₁^2 + I₂^2 Given B_ net = 52 T = 52 10⁻⁶ T , I₁ = 5 A , and I₂ = 12 A : 52 10⁻⁶ = 4 10⁻⁷ 2 d 5^2 + 12^2 52 10⁻⁶ = 2 10⁻