# Q & A: Field direction inside a solenoid

Q:
The relationship between the direction of the lines of force and of the current is expressed in Right hand grip rule. From the magnetic fields of a solenoid and a narrow coil, it is observed that the lines of force are closed loops that are not circular. why is this so? ANd, most of the lines near the centre of the solenoid are almost parallel. why is this so?
- ya chi
A:
I'll answer the second question first:

A solenoid is a name used for a coil of wire wrapped in a helix. Usually the wire spacings are so close that the helix looks very much like a cylinder. The cylinder may have stuff inside (like iron, or maybe just a stiffening tube), or nothing at all.

If the solenoid is very long and thin, then one little segment of the solenoid in the middle looks a lot like another little segment right next to it. Whatever the magnetic field is in that one segment should be the same as in the one next to it. If we are looking at a part of the solenoid near the ends, then there are "edge effects", or "fringe fields", but near the middle, the magnetic field lines do not change from one part of the solenoid to the next. This is called "translational symmetry". There's also a rotational symmetry here. Turn the solenoid around on its axis and the field should be the same.

The magnetic field lines do not start and stop anywhere, because there are no magnetic "charges". Magnetic field lines must travel around moving currents. For this reason, and because of the symmetries mentioned above, the magnetic field lines must all travel parallel to the axis of the solenoid. If a field line were not parallel to the axis, it would either point outwards or inwards. Turning the solenoid around means that all field lines either point outwards or they all point inwards. Moving the solenoid along the axis means this happens for every little bit of the solenoid. But if all the field lines point outwards everywhere, then field lines have to start in the middle of the solenoid. Or they all have to end there. But there are no magnetic charges, so this cannot be.

This isn't quite true at the ends -- the field lines do spread apart there. And what we mean by "near the center" depends on how long the solenoid is and how thin it is. If the solenoid is very short and stubby (just one turn of thin wire, for example), then the field lines won't be particularly straight anywhere, except for that one special one going right up the middle.

The first question is now easy to answer -- since the field lines are straight in the middle of a solenoid, they cannot be also circular! Or more appropriatley, the field lines do in fact bend around outside the solenoid and re-enter the other end. These take a long, smooth path outside, which isn't circular, but at least is more so than the approximately straight field lines inside. The field lines will then look like big letter "D"s.

There will also be a little bit of a twist in the field lines due to the fact that not only does current flow around the loops perpendicular to the axis of the solenoid, but there is also current flowing along the direction of the axis of the solenoid (the wires are arranged in a helix, after all). So if you follow a field from one end of the solenoid to the other, and around outside back in, you won't quite end up where you started -- the field lines in general won't be closed loops.

Tom

(published on 10/22/2007)