Electricity, Magnetism and Electromagnetism, Ch Ampère's law, magnetic flux and the shape of the magnetic field
Problem
A sketch of a proposed static magnetic field shows straight field lines pointing radially outwards from a long straight axis, all lying in planes perpendicular to the axis. The spacing of the lines says the magnitude falls as 1/s, where s is the perpendicular distance from the axis. Written out, the proposal isB=sCs^,C=2.0×10−5Tm,with s^ the unit vector pointing away from the axis. Test the sketch against both magnetic laws.
((a)) Take the closed surface of a cylinder of radius 4.0cm and length 10cm, coaxial with the axis, with the outward normal. Calculate the net magnetic flux out of it.
((b)) Take the circle of radius 4.0cm centred on the axis, in a plane perpendicular to it. Calculate the circulation ∮B⋅dl round it.
((c)) Could this pattern be a static magnetic field? Name the law it fails and the law it satisfies.