Re: How do magnetic fields work in terms of shape? Also - sparks seen

We can not see the magnetic field. I think when you say "all magnetic
fields are in a closed circular shape", what you really mean is the
magnetic field lines, which are used to depict the magnetic field
in many physics books.

The magnetic field fills the whole space. It has different strengths and 
directions at different points. If we hold a very small bar magnet in the
magnetic field and our feeling is sensitive enough, we can feel an 
torque and force on the magnet. The torque tries to rotate the magnet 
until its axis (the line through its two poles) becomes parallel to a 
specific direction, which is the direction of the magnetic field at that
point. The force tries to move the magnet to a new position where the 
strength of the magnetic field is greater. If we draw such curves whose 
tangential line always agrees with the direction of the magnetic field, 
we'll see these curves are always closed, but not always circular. These 
curves are called magnetic field lines.

Therefore, the magnetic field lines are only visual aid for understanding
variation of the direction and strength of the magnetic field in the space.
The closed-ness of the magnetic field line does have an implication for
the characteristics of the magnetic field, that is, there is no magnetic
charge or magnetic monopole in the world, unlike the electric field.
All the magnetic fields are essentially generated by electric currents
and circle around the currents. You may wonder about the magnetic
field generated by a permanent magnet. Actually it is gnerated by the
spin of the electrons in the permanent magnet, which can also be regarded
as a kind of current.

This rule is called Ampere's Law[1] and it has a beautiful mathematical 
representation. However there is still a large distance to the practicle
calculation of the magnetic field. There is another rule called 
Bio-Savart Law for practical applications. It may look a bit tedious,
but actually it is easy to use. If you know the currents, you only need
an integration, which is actually just cutting the current into small
pieces and then summing up the magnetic field generated by each piece.

As to the spark, I think there are several possibilities: it may be 
caused by static charges or voltage difference between the electromagnet 
and the permanent magnet, and it may be caused by sudden changes
of the magnetic field. It is easy to determine whether it is related 
to the magnetic field. Since magnetic field itself does not generate
electric field and only its variation can generate electric field 
(Faraday's Law[3]), if the sparks only appears when you switch on or 
off the electromagnet, it is most probably caused by the varation of 
the magnetic field. But if the sparks appear even when there is no 
current change in the electromagnet, you can try measuring the voltage 
difference between the electromagnet and the permanent magnet since 
there may be some electric leakage.

[1-3]http://www.treasure-troves.com/physics/physics.html