Re: How does the magnetic field of a gas giant evolve?

   A wonderful trio of questions!  Magnetic fields in planets are not 
totally understood.  However, we have a pretty good idea of the basics, so 
I'll give you the best answer I can.
   First of all, I'd like to explain a little of how magnetic fields are 
produced in planets right now.  The basic theory is that fluid interiors of 
at least some planets are able to carry currents (moving charges).  A 
basic result of electricity and magnetism is that whenever you have a 
moving charge, you have a magnetic field produced.  This field turns out to 
affect the moving charges, which then affects the field, and so forth (this 
is the major complication and the reason we don't totally understand 
things).  But the basic idea is that you need these moving charges.  So 
what you really must have are:
     1.   A fluid interior.  It turns out it has to have rising and falling 
motions (away from and towards the center of the planet) called convection 
(you can see convection in a pot of boiling water).  Convection results 
from heating within the planet; this point will come up shortly.
     2.   The fluid needs to be able to carry currents.  This means, in 
short, a metallaic fluid.  For the Earth and Mercury (which both have 
fields), the metal is iron and nickel.  It isn't so clear at first what 
metal could be in a gas giant.  But it turns out that it's hydrogen.  We 
usually think of hydrogen as not a metal, but under enough pressure, it 
begins to conduct electrons just like any metal.  These pressures can be 
achieved in the gas giants.
     3.  Rotation.  It turns out that a planet needs to rotate to get the 
field (part of the moving in "moving charges").  This is possibly why Venus 
doesn't have a magnetic field (it rotates extremely slowly).

   Ok, knowing that about magnetic fields today, we can ask where they came 
from at all.  It is believed that there may have been an external magentic 
field early in our solar system's history, perhaps from the young sun.  
This extrenal field may have caused the charged particles in the planets' 
interiors to change directions (with the positive and negative charges 
moving off in opposite directions).  Once the positive and negative charges 
split up, the could produce currents (if you have all the positive and 
negative charges moving together, there is no net current because they 
cancel each other out).  The currents produce a field, which case more 
effects on the currents... and so forth, so that even after the external 
field was removed, the planet continued to generate a field.
    The time evolution of fields is really tough.  For example, we know 
from geological records that the Earth's field changes direction 
periodically.  But its not quite certain why exactly this happens.  As far 
as I know, there is no evidence that this happens in the gas giants  But we 
have no reason not to think it should, assuming the Earth's field is 
similar to the gas giants'.
    We can try to figure out what ends a magnetic field, though.  Looking 
at the above three items needed for at magentic field, 2 and 3 don't change 
much with time and are unlikely to be the death of any planet's field.  
However, item 1 is not constant.  To have a convecting, fluid interior, you 
need an internal heat source.  In the Earth, this is from radioactive 
decays in the rocks (not a lot of it in any chunck of rock, but the Earth 
is huge and so there is a lot of heat total).  In the gas giants, this 
plays a minor role (hydrogen and helium aren't usually radioactive).  In 
those cases, it is thought that the heat froms from the planets shrinking 
slowly through time (we are pretty sure that something like this is 
happening, since Jupiter gives off around three times as much heat as it 
recieves from the sun).
    Eventually, these heat sourves won't be enough to keep the planet's 
interior convecting (and eventually they will be too cold to be fluids).  
This has already happened to Mars, which may have once had a magnetic 
field, but no longer has enough heat to convect.
    There are probably dozens of answer for the final question; magnetic 
fields have many effects, but I'll try to list a few:
     *  Magnetic fields deflect incoming charged particles away from the 
planet.  These particles could be from the sun (many are) or from deep 
space.  In Earth's case, this may be a major factor in protecting life on 
the surface from damaging particles that would otherwise cause genetic 
damage and cancer.  Eventually, humans may find this useful out amoung the 
gas giants!
     *  These deflections can send particles to the planet's poles, leading 
to aurorae.  Aurora have been obsevered on Jupiter as well as Earth.  Not a 
terrifically important effect, but really pretty!
     *  The deflection of particles may also protect the upper atmospheres 
of planets from these particles, which would otherwise strip away the 
uppermost portions of atmospheres.
     *  Magnetic fields exhert pulls on rings particles and on charged 
particles in orbit about the planets.  In the latter case, this leads to 
things like a large ring of charged particles from the moon Io, trapped 
around Jupiter.
     * Magnetic fields also can affect man-made probes in nasty ways 
(either directly or by the particles they trap).  This happened to Galileo 
on Thanksgiving Day 1999, much to NASA's dismay (they did recover the 
spacecraft).

   There are certainly more effects, here, but these are some of the ones 
that strike me as most interesting.  Magnetic fields do not, however, 
really influence the shape of a planet.  The shape is bascially all from 
gravity pulling inwards and pressure and rotation pressing outwards.

   Two books that have some good stuff on this topic:
   "Moons and Planets" by William K. Hartmann
   "The Cosmic Perspective", by Bennett, Donahue, Schneider and Voit.
   Both are textbooks, so they may be a bit hard to find, but they book 
explain some of this fairly well.
   Sorry that this response was so long; good questions sometime require 
long answers!