Two long straight parallel conductors carry currents ' I ₁ ^ and ' I ₂ ^ ( I ₁> I ₂ ) . When direction of ' I ₁ ' and ' I ₂ ' is same, the magnetic field intensity midway between two conductors is 20 ~T . If direction of ' I ₂ ' is reversed, the field intensity becomes 50 ~T . The ratio I ₂ / I ₁ is

Step-by-step solution

The magnetic field intensity at the midway point between two parallel conductors separated by distance d is considered. Each field contribution follows B = ₀ I 2 r , with r = d/2 at the midpoint. For currents flowing in the same direction, the magnetic fields oppose, yielding a net field: B_ net = ₀ d (I₁ - I₂) = 20 , T . Reversing I₂ aligns the fields, giving: B_ net = ₀ d (I₁ + I₂) = 50 , T . Dividing these equations eliminates the common factor: I₁ - I₂ I₁ + I₂ = 2 5 . Solving yields 5(I₁ - I₂) = 2(I₁ + I₂) , wh