Two long parallel wires carrying currents 8 A and 15 A in opposite directions are placed at a distance of 7 cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnetic field at P is ___ 10⁻⁶ T. (Given: 2 = 1.4 , ₀ = 4 10⁻⁷ SI unit)

Step-by-step solution

Let the distance of point P from each wire be r . Since the lines joining P to the wires are perpendicular, they form a right-angled isosceles triangle with the distance between the wires as the hypotenuse. r^2 + r^2 = d^2 2r^2 = (7 10⁻²)^2 r = 7 2 10⁻² m The magnetic fields due to the two wires at point P are: B₁ = ₀ I₁ 2 r and B₂ = ₀ I₂ 2 r Since the position vectors from the wires to point P are perpendicular to each other, the magnetic field vectors B ₁ and B ₂ are also perpendicular to each other. The net magn