Electricity, Magnetism and Electromagnetism, Ch Ampère's law, magnetic flux and the shape of the magnetic field
Problem
A cylindrical bar magnet of radius 8.0mm and length 60mm is magnetised along its axis. Across the mid cross-section of the bar the field inside the material is uniform over the cross-section, of magnitude 0.30T, and points along the axis from the south end towards the north end. All fields are steady. A student says: "Field lines start at a north pole. So a closed surface that encloses only the north half of this magnet must have a net outward flux, and if I cut the magnet in half at the middle I shall be left with an isolated north pole." Take the closed surface S to be a cylinder of radius 8.0mm coaxial with the magnet, one flat end being the mid cross-section of the magnet and the other flat end lying in air 20mm beyond the north end face, so that S encloses the north half of the bar. Use the outward normal.
((a)) Calculate the flux of B out of S through the flat end that lies in the mid cross-section of the magnet.
((b)) State the net flux out of S, with the law you use.
((c)) Hence find the total flux out of S through the remaining parts of the surface (the curved side and the far flat end), and say in one sentence what cutting the magnet in half actually produces.