Brad, Itsu, PM, F6, Guys, You are comparing apples to oranges. Field lines are lines of force, and here we have two different lines of force. First off the B field lines show the direction of a force that would apply to an isolated magnetic N pole. Such an isolated N pole would be repelled from the N pole of the magnet and would travel along one of those field lines to reach the S pole of the magnet. We don't have isolated poles but you can do an experiment that will show this effect. Make a long thin magnet by magnetizing a length of rigid piano wire, then suspend this from a ceiling so that it hangs down as a pendulum with the S pole at the suspension point, a pendulum that can follow the surface of a cone. Then place a small magnet directly below it to see the N pole of the pendulum repelled from the N pole of the magnet. You will see that N pole follow a curved trajectory as depicted in the rather poor image attached. That is showing you the B field line. It is a line of force and if you integrate that line from The N pole of the magnet to the S pole you get the energy (force times distance) or work done. So from that starting position there is that potential energy available. It is not just some vague potential, it is potential energy. If you started somewhere else on the force line you would get less potential energy. If you wanted to you could draw other "field" lines like lines of equipotential energy. Iron filings are magnetized by the B field to become tiny magnets and they do link up to form strings that follow those B lines.
Brad's figure of eight field lines are a different field. They are not the force on an isolated N pole, they are the force on a line element of current. Brad is correct to see them as field lines, and to call them magnetic field lines as clearly they come from magnetism. They need a different terminology. We already have magnetic A fields, magnetic B fields and magnetic H fields. Perhaps we should call them F8 fields because of that figure of 8. Or maybe we could use FLH fields as they obey Fleming's LH rule. Or why not just magnetic F field? Since by Fleming's LH rule the force is always at right angles to the B field, you can easily plot the F field lines as shown in the second image. And being lines of force there is potential energy available so you could also plot lines of equipotential energy of you wanted to. Smudge
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