What are the magnetic poles of the $B$-fields in these electric current diagrams?

Question

What is the geometry of the magnetic fields $B$ in these diagrams - where do magnetic north and south face? http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/wirfor.html

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html

Are they oscillating, or random, at each point on the current flow? Is that why you have to coil wires around to create an electromagnet: https://en.wikipedia.org/wiki/Electromagnet

So that instead of an oscillating or haphazard magnetic alignment, you get a stable north-south alignment that can attract metal?

Are there any diagrams of what the magnetic field looks like here?

Answer 1

In the first diagram, imagine a piece of paper spanning the gap between the wires. The North Pole is all over the far side of the paper (the side you can't see) and the South Pole is all over the near side. This because the South Pole is the region into which the field lines converge before they emerge, spreading out, from the North Pole. It's slightly artificial calling these areas (the two sides of the paper) 'poles', because they are so spread out. The thickness of the piece of paper, that is the separation of the poles, is also arbitrary.

The second diagram shows two separate current-carrying wires. These can't be assigned North or South poles as there is no region from which field lines emerge, spreading out, or into which they converge. Because the lines are circular every region around the wire is the same as every other region and there is no convergence or spreading out.

For solenoids (helically coiled wires) the North pole (area from which the magnetic field lines diverge and South Pole (area to which they converge) are quite small, roughly (but not exactly) co-inciding with the geometric ends of the solenoid.

The ends of a solenoid, like the poles of a magnet, will attract pieces of iron because two conditions are fulfilled here: (a) the field is strong, so will induce strong alignment of domains in the iron (b) the field is strongly non-uniform causing a resultant force on the magnetised iron, rather than just a torque.

So the pattern of magnetic field lines tells you where, if at all, the poles are situated. The pattern of field lines can be deduced from the configuration of electric currents using the Biot-Savart law or equivalent.