A long straight solid cylindrical wire of radius R carries a steady current I uniformly distributed across its cross-section. Let B₁ be the magnitude of the magnetic field at a distance r₁ = R 2 from the axis of the wire, and B₂ be the magnitude of the magnetic field at a distance r₂ = 2R from the axis. The ratio B₁ : B₂ is

Step-by-step solution

For a point inside the wire ( r At r₁ = R 2 , the magnetic field is: B₁ = ₀ I ( R 2 ) 2 R^2 = ₀ I 4 R For a point outside the wire ( r > R ), the magnetic field is given by B = ₀ I 2 r . At r₂ = 2R , the magnetic field is: B₂ = ₀ I 2 (2R) = ₀ I 4 R Taking the ratio: B₁ B₂ = ₀ I 4 R ₀ I 4 R = 1 Thus, B₁ : B₂ = 1 : 1 . Answer: 1 : 1