Two long, parallel wires carry currents i₁ and i₂ such that i₁ > i₂ . The magnetic field at a midway point between the wires is 10 T when the currents travel in the same direction. If the direction of i₂ is reversed, the magnetic field becomes 30 T . Determine the ratio i₁/i₂ .

Step-by-step solution

Let the distance between the wires be 2d . The magnetic field at the midway point due to a long straight wire carrying current i is B = ₀ i 2 d . When the currents are in the same direction, the magnetic fields at the midway point oppose each other. Since i₁ > i₂ , the net magnetic field is: B₁ = ₀ 2 d (i₁ - i₂) = 10 T When the direction of i₂ is reversed, the currents are in opposite directions, and their magnetic fields at the midway point add up: B₂ = ₀ 2 d (i₁ + i₂) = 30 T Dividing the two equations, we get: i₁