QUESTION:
I would like to know if the particles and rocks forming the rings are
now slowly falling into Jupiter, and eventually the rings will be gone?

ANSWER from Elias Barbinis on April 14, 1997:
Jupiter's rings are formed by charged particles of various sizes. Most
of these particles are very tiny (about 1 micron across). There are two
forces that are exerted on these particles by Jupiter:  a
gravitational force and an electromagnetic force. The gravitational
force is stronger than the electromagnetic force for particles with
size of 1 micron and it provides the centripetal accelaration that is
required to keep these particles in circular motion around Jupiter.
Throughout their lifetime these particles are ground down by the
energetic particles that are abundant in Jupiter's magnetosphere and
eventually they become so small (about 0.03 micron across) that the
electromagnetic force overpowers the gravitational force and the
particles leave the rings and fall into Jupiter's atmosphere. The
lifetime of these particles is about 1000 years, which is very short
in a cosmological sense. However, Jupiter's rings are a permanent
feature because these tiny particles are regenerated continually by
collisions of interplanetary micrometeoroids with boulder-size objects
within the rings.