A long straight wire of radius 'r' carries a steady current 'I'. The current is uniformly distributed over its cross-section. The ratio ( B B^1 ) of the magnetic field ' B ' and ' B^1 ' it radial distances r 2 ' and ' 3 r ' respectively, from the axis of the wire is

Step-by-step solution

For a long straight wire carrying uniform current I with radius r , the magnetic field varies with radial distance r' from the axis. The field inside the wire ( r' r ) it follows B = ₀ I 2 r' . At distance r' = r/2 (inside the wire): B = ₀ I (r/2) 2 r^2 = ₀ I 4 r At distance r' = 3r (outside the wire): B' = ₀ I 2 (3r) = ₀ I 6 r The ratio is then: B B' = ₀ I 4 r ₀ I 6 r = 1/4 1/6 = 3 2 Final answer: B