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)
