A long straight solid cylindrical wire of radius R carries a steady uniform current along its length. If the magnitude of the magnetic field at a radial distance r₁ = R 2 from the axis is B₁ , and at a radial distance r₂ = 2R from the axis is B₂ , then the ratio B₁ : B₂ is:

Step-by-step solution

For a solid cylinder of radius R carrying a uniform current I : The magnetic field inside the wire ( r At r₁ = R 2 , B₁ = ₀ I ( R 2 ) 2 R^2 = ₀ I 4 R . The magnetic field outside the wire ( r > R ) is B = ₀ I 2 r . At r₂ = 2R , B₂ = ₀ I 2 (2R) = ₀ I 4 R . Therefore, the ratio B₁ B₂ = ₀ I 4 R ₀ I 4 R = 1 : 1 . Answer: 1 : 1