A long straight solid cylindrical conductor of radius R carries a steady uniform current along its length. If the magnitude of the magnetic field at a radial distance of R 2 from the axis of the conductor is B₀ , what will be the magnitude of the magnetic field at a radial distance of 3R from the axis?

Step-by-step solution

For a solid cylindrical conductor of radius R carrying a steady current I , the magnetic field inside the conductor ( r B_ in = ₀ I r 2 R² At r = R 2 : B₀ = ₀ I ( R 2 ) 2 R² = ₀ I 4 R From this, we get ₀ I = 4 R B₀ . The magnetic field outside the conductor ( r > R ) is given by: B_ out = ₀ I 2 r At r = 3R : B = ₀ I 2 (3R) = ₀ I 6 R Substituting the value of ₀ I : B = 4 R B₀ 6 R = 2 3 B₀ Answer: 2B₀ 3