A long straight solid cylindrical wire of radius a carries a steady uniform current I . The magnitude of the magnetic field is maximum at the surface of the wire. At which of the following pairs of radial distances from the axis of the wire is the magnitude of the magnetic field exactly one-third of its maximum value?

Step-by-step solution

The magnetic field due to a long straight solid cylindrical wire of radius a carrying a steady uniform current I is maximum at its surface ( r = a ). Maximum magnetic field, B_ max = ₀ I 2 a Inside the wire ( r B_ in = ₀ I r 2 a^2 = B_ max ( r a ) We are given that B_ in = B_ max 3 . B_ max ( r a ) = B_ max 3 r = a 3 Outside the wire ( r > a ), the magnetic field is given by: B_ out = ₀ I 2 r = B_ max ( a r ) We are given that B_ out = B_ max 3 . B_ max ( a r ) = B_ max 3 r = 3a Therefore, the magnitude of the magn