Two long parallel wires separated by a distance of 10 cm carry currents of 6 A and 8 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. A charged particle of charge 2 C is projected from P with a velocity of 5 10^5 m/s in a direction parallel to the wires. The magnitude of the magnetic force on the charge is X 2 10⁻⁶

Step-by-step solution

Let the distance of point P from each wire be d . Since the lines joining P to the wires are perpendicular, they form a right-angled triangle with the distance between the wires as the hypotenuse. d^2 + d^2 = (10 cm )^2 2d^2 = 100 d = 5 2 cm = 5 2 10⁻² m The magnetic fields due to the two wires at P are perpendicular to each other. The net magnetic field is: B_ net = B₁^2 + B₂^2 = ₀ 2 d I₁^2 + I₂^2 B_ net = 2 10⁻⁷ 5 2 10⁻² 6^2 + 8^2 = 2 10⁻⁷ 5 2 10⁻² 10 B_ net = 20 10⁻⁷ 5 2 10⁻² = 2 2 10⁻⁵ T Since the wires are par