Polarization Inside a Dielectric

Slide a slab of plastic between charged capacitor plates and the capacitor suddenly holds more charge at the same voltage, or needs less voltage to hold the same charge. Nothing about the plates changed. What changed is the field in the gap, and that comes down to what the slab's molecules do when they feel that field.

A dielectric is an insulator, so its electrons cannot roam. But each molecule still responds: its negative charge shifts slightly toward the positive plate, its positive charge shifts slightly toward the negative plate. Stack up trillions of these tiny stretched molecules and the surfaces of the slab end up with a thin layer of bound charge, negative facing the positive plate, positive facing the negative plate. That layer makes its own electric field, pointing opposite the original field from the plates. The two fields partly cancel, so the net field inside the dielectric is weaker than it was in vacuum, specifically smaller by a factor of kappa, the dielectric constant. Weaker field at the same charge means the plates can hold more charge before reaching the same voltage, which is exactly why inserting a dielectric raises a capacitor's capacitance.

This sets up the next idea directly: since C = Q/V and V dropped by a factor of kappa for the same Q, capacitance scales up by kappa. It also explains why dielectrics have a breakdown limit: push the field hard enough and the slab's bound electrons get ripped free, turning the insulator into a conductor and ruining the capacitor.