Dielectrics and capacitor energy

A capacitor stores charge by keeping two conductors apart, and its capacitance — how much charge it holds per volt of applied voltage — depends on the plates' geometry and on whatever fills the gap between them. A dielectric is an insulating material that, placed in that gap, does something useful precisely because it does not conduct: its molecules polarise in response to the field, lining up to partially oppose it. The field between the plates weakens as a result, and since capacitance is charge divided by voltage, a weaker field for the same charge means a lower voltage, which means a higher capacitance. The intuitive guess — that stuffing something into the gap should reduce capacitance by getting in the way — has the physics backwards.

The energy a charged capacitor stores is U = ½CV², and the exponent on V matters for the same reason it mattered for resistive power: doubling the voltage across a capacitor quadruples the energy stored, not doubles it. This is why capacitors used to store significant energy — camera flashes, defibrillators — are rated for a specific voltage and why exceeding it is dangerous out of proportion to how much the voltage rose.

Real capacitors almost always use a dielectric rather than a vacuum or air gap for two compounding reasons: the increased capacitance packs more storage into the same physical size, and most dielectrics can withstand a stronger field before breaking down than air can, which lets the plates be brought closer together for even more capacitance. Both effects push the same direction, which is why dielectric choice is one of the main design decisions in practical capacitors.