2.3 Electric Permittivity

What permittivity means

Electric permittivity (ε) measures how a material responds to an electric field — how much it allows field lines to pass through versus how it resists or reorganizes them. In a vacuum, this constant is ε₀ = 8.85 × 10⁻¹² C²/(N·m²), used in Coulomb's law and Gauss's law formulas as the baseline for calculating electric forces and fields.

Permittivity in materials (dielectrics)

When a material (a dielectric) is placed in an electric field, its molecules polarize, creating an internal field that partially opposes the external one. This reduces the net field inside the material. A material's permittivity ε is usually greater than ε₀, and the ratio ε/ε₀ is called the dielectric constant (κ), showing how much the material weakens the field compared to vacuum.

Why permittivity matters

Permittivity appears in Coulomb's law (F = q₁q₂/(4πεr²)) and in capacitor equations, where inserting a dielectric between capacitor plates increases capacitance because ε increases and reduces the effective field, allowing more charge storage at the same voltage. Higher permittivity means weaker forces/fields for a given charge distribution within that medium.

Key terms

Electric permittivity (ε)

A measure of how much a material allows or resists an electric field; used in Coulomb's law and capacitor equations.

Permittivity of free space (ε₀)

≈ 8.85 × 10⁻¹² C²/(N·m²); the baseline permittivity value for a vacuum.

Dielectric

A material whose molecules polarize in an external electric field, creating an opposing internal field that reduces the net field.

Dielectric constant (κ)

The ratio ε/ε₀; shows how much a material's permittivity exceeds that of a vacuum.

Effect of higher permittivity on capacitors

Increases capacitance by weakening the internal field, allowing more charge to be stored at the same voltage.

Try an AP-style question

Coulomb's constant k equals which expression?

1. 4πε₀
2. 1/(4πε₀)
3. 1/ε₀
4. ε₀/4π