A long straight solid cylindrical conductor of radius R carries a steady current uniformly distributed over its cross-section. The magnitude of the magnetic field at a distance r = R 4 from the axis of the conductor is B . At what distance from the axis, outside the conductor, will the magnitude of the magnetic field again be equal to B ?

Step-by-step solution

For a long straight solid cylindrical conductor of radius R carrying a steady current I uniformly distributed over its cross-section, the magnetic field at a distance r from the axis is given by Ampere's law. Inside the conductor ( r B_ in = ₀ I r 2 R^2 Outside the conductor ( r > R ): B_ out = ₀ I 2 r At a distance r = R 4 inside the conductor, the magnetic field is: B = ₀ I 2 R^2 ( R 4 ) = ₀ I 8 R Let the distance outside the conductor where the magnetic field is again B be r' . Then: B_ out = ₀ I 2 r' = B Substi