Two identical long parallel wires carry currents I₁ and I₂ such that I₁>I₂ . When the currents are in the same direction, the magnetic field at a point midway between the wires is 6 10⁻⁶ ~T . If the direction of I₂ is reversed, the field becomes 3 10⁻⁵ ~T . The ratio ( I₁ I₂ ) is-

Step-by-step solution

Using ampere's law: B I and B 1 / d . For two wires separated by a distance d , if B₁ is the field when the currents are in the same direction and B₂ is the field when currents are in opposite directions, then B₁ B₂ = ₀ 2 ( i₁ d - i₂ d ) ₀ 2 ( i₁ d + i₂ d ) = 1 5 On solving: aligned & ( i₁ i₂ -1 ) ( i₁ i₂ +1 ) = 1 5 & i₁ i₂ = 3 2 aligned