Saturn has rings. Its moons do not. The question of why moons orbiting within planetary magnetospheres lack ring systems has a surprisingly simple electromagnetic answer.
Erak and Rozner show that the electric field induced by the rotation of the ambient planetary magnetosphere strips charged particles from circumsatellital orbits. A ring particle orbiting a moon inherits the moon's orbital velocity but also sits in the planet's rotating magnetic field. The relative motion between the particle and the magnetosphere induces an electric force. For sufficiently charged grains — and ring particles acquire charge through UV irradiation and plasma sputtering — this electric force exceeds the gravitational binding to the moon. The particles are swept away.
The mechanism is not a slow erosion. The removal timescale for micron-scale charged grains can be short compared to the age of the Solar System. The magnetic field doesn't gradually degrade the ring — it prevents the ring from accumulating in the first place. Any material shed from the moon's surface or captured from passing debris gets electrically cleaned before it can build up into a visible ring structure.
The constraint depends on the planet's magnetic field strength, the moon's distance from the planet, the particle size, and the charging environment. Moons far from the planet (where the magnetosphere is weaker) or large particles (which carry less charge per unit mass) are less affected. This predicts a zone around each giant planet where circumsatellital rings are magnetically forbidden — close enough for the induced electric field to dominate — and an outer zone where rings are electromagnetically possible.
The planet's magnetic field is both a shield and a cage. It protects its moons from solar wind but prevents them from wearing jewelry.