Two long parallel wires carry currents I ₁ and I ₂ ( I ₁> I ₂ ) . When currents are flowing in the same direction, the magnetic field at a point midway between the wires is 6 10⁻⁶ ~T . If the direction of I ₂ is reversed the field at midpoint becomes 3 10⁻⁵ ~T . The ratio I ₁: I ₂ is

Step-by-step solution

Let 2d be the distance between the parallel wires. The magnetic field at the midpoint due to a single wire carrying current I is B = ₀ I 2 d . Case 1: Currents in same direction When currents flow in the same direction, their magnetic fields oppose at the midpoint. Since I₁ > I₂ , the net field is B₁ - B₂ = ₀ 2 d (I₁ - I₂) = 6 10⁻⁶ T . Case 2: Currents in opposite directions When I₂ is reversed, the fields reinforce, giving B₁ + B₂ = ₀ 2 d (I₁ + I₂) = 3 10⁻⁵ T . Dividing the second equation by the first yields I₁ +