Dielectrics

What is a dielectric?

A dielectric is an insulating material placed between conductors, often between capacitor plates. Unlike a conductor, a dielectric does not allow charges to move freely over large distances. However, its molecules can polarize in response to an electric field.

Polarization means positive and negative charges shift slightly in opposite directions inside atoms or molecules, or permanent molecular dipoles partially align with the field.

Polarization and bound charge

When a dielectric polarizes, bound charges appear on its surfaces. These are not free charges supplied by a battery; they are small separations of charge within the material. The bound charge creates an electric field that opposes the original field inside the dielectric.

As a result, the net electric field inside the material is reduced compared with the field that would exist in vacuum for the same free charge on the plates.

Dielectric constant

For a linear dielectric, the electric field is reduced by a factor called the dielectric constant, or relative permittivity, written $kappa$:

E=rac{E_0}{kappa}

where $E_0$ is the field without the dielectric. The permittivity of the material is

$epsilon=kappaepsilon_0$

Most ordinary dielectrics have $kappa>1$.

Capacitance with a dielectric

For a parallel-plate capacitor completely filled with a dielectric,

$C=kappa C_0$

where $C_0$ is the capacitance without the dielectric. Since

C_0=rac{epsilon_0 A}{d}

the dielectric-filled capacitance is

C=rac{kappaepsilon_0 A}{d}=rac{epsilon A}{d}

Thus inserting a dielectric increases capacitance.

Fixed charge case

If a charged capacitor is isolated, its charge $Q$ remains fixed. Inserting a dielectric increases $C$, so the voltage decreases:

Delta V=rac{Q}{C}

The electric field also decreases. The stored energy decreases, and the dielectric is pulled into the capacitor. The missing energy appears as mechanical work or other energy transfers.

Battery connected case

If the capacitor remains connected to a battery, the voltage stays fixed. Inserting a dielectric increases $C$, so more charge flows onto the plates:

$Q=CDelta V$

The electric field set by plate voltage and separation may remain approximately fixed for a parallel-plate geometry, while free charge increases to support that field in the dielectric.

Dielectric strength

Every dielectric has a maximum electric field it can withstand before breakdown. This is called dielectric strength. If the field is too large, the material ionizes or conducts, allowing discharge. Lightning is dielectric breakdown of air.

Capacitors are rated for maximum voltage to avoid breakdown.

Microscopic energy view

The dielectric reduces field energy for a fixed free charge by allowing polarization. The field does work polarizing the material, and the material changes the relationship between free charge and voltage. This is why dielectrics are essential for making compact capacitors with large capacitance.

The big idea

Dielectrics are insulating materials that polarize in electric fields. Their polarization reduces internal electric field for fixed free charge and increases capacitance. The dielectric constant describes this effect, while dielectric strength limits how much field the material can tolerate before breakdown.