Two parallel wires separated by a distance of 10 cm carry currents of 10 A and 40 A in the same direction. At what position should a third current be placed such that it experiences zero magnetic force?

Step-by-step solution

Let the third wire be placed at a distance x from the 10 A wire. For the third wire to experience zero magnetic force, the net magnetic field at its position must be zero. Since the currents in the two wires are in the same direction, the magnetic fields produced by them will be in opposite directions only in the region between the wires. Equating the magnitudes of the magnetic fields produced by the two wires at distance x from the 10 A wire: B₁ = B₂ ₀ I₁ 2 x = ₀ I₂ 2 (d - x) Substituting I₁ = 10 A , I₂ = 40 A , a