3.3 Dielectrics

Dielectrics reduce the field

A dielectric is an insulating material inserted between capacitor plates. Its molecules polarize in response to the external field, creating an internal field that opposes it. This reduces the net electric field inside by a factor of the dielectric constant κ (kappa), where κ ≥ 1. For an isolated charged capacitor, E = E₀/κ.

Capacitance increases with κ

Since C = Q/V and V decreases (E decreases) while Q stays fixed on an isolated capacitor, capacitance increases: C = κC₀, where C₀ is the vacuum/air capacitance. For a parallel plate capacitor, C = κε₀A/d. Dielectrics also let capacitors hold more charge without breaking down (higher dielectric strength).

Two scenarios: battery vs. isolated

If a capacitor stays connected to a battery (constant V), inserting a dielectric increases C and Q = CV increases, while V stays fixed. If the capacitor is isolated (constant Q), inserting a dielectric decreases V and E by factor κ, while Q stays fixed. Energy stored: U = Q²/2C decreases if Q constant; U = ½CV² increases if V constant.

Key terms

Dielectric

An insulating material placed between capacitor plates that polarizes to reduce the net electric field.

Dielectric constant (κ)

A dimensionless factor (κ ≥ 1) describing how much a material reduces the electric field and increases capacitance: C = κC₀.

Effect on isolated (constant Q) capacitor

Inserting a dielectric decreases E and V by factor κ; Q stays constant; stored energy decreases.

Effect on battery-connected (constant V) capacitor

Inserting a dielectric increases C and Q; V stays constant; stored energy increases.

Dielectric strength

The maximum electric field a dielectric material can withstand before it breaks down and becomes conductive.

Try an AP-style question

A dielectric with κ = 3 fills a capacitor. What happens to its capacitance?

1. It is divided by 3
2. It stays the same
3. It is multiplied by 9
4. It triples