Dielectrics and Polarisation
When you place an insulating material — like glass, rubber, or paper — between the plates of a capacitor, something remarkable happens: the capacitor can store significantly more charge than it could with just empty space. The reason lies in a phenomenon called polarisation. Unlike conductors, where electrons flow freely, the electrons in an insulator are tightly bound to their atoms. However, an external electric field can still push those electrons slightly out of their equilibrium positions, creating tiny electric dipoles throughout the material. This collective response is what physicists call dielectric polarisation, and the material itself is called a dielectric. Think of polarisation like a crowd of people all tilting slightly in the same direction when a wind blows — no one walks anywhere, but there is a collective shift. In a dielectric, each atom or molecule develops a small separation between its positive nucleus and its negative electron cloud. These microscopic dipoles all align (partially) with the applied field, producing an internal electric field that opposes the original one. The net effect is that the electric field inside the dielectric is weaker than it would be in a vacuum, which allows the capacitor to store more charge at the same voltage. The strength of a material's dielectric response is quantified by its relative permittivity (also called the dielectric constant), symbol εᵣ. Vacuum has εᵣ = 1 by definition; water has εᵣ ≈ 80, meaning water molecules polarise so strongly that the electric field inside is reduced to about 1/80 of its free-space value. Understanding dielectrics is essential for designing capacitors, insulating cables, and modern electronic components — it sits at the heart of much of today's electronic technology.
- The Unpolarised State
- Applying an External Field
- Formation of Electric Dipoles
- The Polarisation Vector P
- Bound Surface Charges and the Opposing Field
- Effect on Capacitance
The Unpolarised State
In the absence of an external electric field, the atoms and molecules of an insulator have their positive and negative charge centres coinciding on average. The material has no net electric dipole moment — it is electrically neutral everywhere, both macroscopically and on average microscopically.
Applying an External Field
When an external electric field E₀ is applied (for example, by connecting a battery to capacitor plates), it exerts a force on positive charges in one direction and on negative charges in the opposite direction. Because the electrons in a dielectric cannot migrate freely, they instead shift very slightly — typically by fractions of an atomic radius — relative to their nuclei.
Formation of Electric Dipoles
Each atom or molecule acquires a tiny electric dipole moment p = αε₀E, where α is the polarisability of that atom/molecule. A dipole moment points from the negative charge to the positive charge. In polar molecules like water (H₂O), permanent dipoles already exist and simply rotate to align with the field — this is orientational polarisation. In non-polar atoms like argon, the distortion of the electron cloud creates an induced dipole — this is electronic polarisation.
The Polarisation Vector P
The macroscopic polarisation P is defined as the dipole moment per unit volume: P = nαε₀E, where n is the number of dipoles per unit volume. The units of P are C/m². Physically, P represents how densely the material is 'filled' with aligned dipoles. A larger P means more charge separation per unit volume.
Bound Surface Charges and the Opposing Field
The aligned dipoles effectively place positive charge on one face of the dielectric and negative charge on the other — these are called bound surface charges (density σ_b = P·n̂, where n̂ is the outward normal). These bound charges produce their own electric field E_P that points opposite to the applied field E₀. The total field inside the dielectric is E = E₀ − E_P = E₀/εᵣ, which is reduced by the factor εᵣ.
Effect on Capacitance
For a parallel-plate capacitor with plate area A and separation d, inserting a dielectric of relative permittivity εᵣ increases the capacitance from C₀ = ε₀A/d to C = εᵣε₀A/d. Since more charge Q = CV can be stored at the same voltage V, the dielectric dramatically increases energy storage. This is why real capacitors are filled with dielectric materials rather than left as air gaps.
The Key Equation
- C — Capacitance (Farads (F)): The ability of the capacitor to store charge per unit voltage.
- \varepsilon_r — Relative permittivity (dielectric constant) (Dimensionless): A material property expressing how much more charge the capacitor can store compared to vacuum. Always ≥ 1.
- \varepsilon_0 — Permittivity of free space (F/m): The fundamental constant ε₀ = 8.85 × 10⁻¹² F/m, describing how well a vacuum supports an electric field.
- A — Plate area (m²): The overlapping surface area of the two conducting plates.
- d — Plate separation (m): The distance between the two parallel plates.
Worked Example
Problem. A parallel-plate capacitor has square plates of side 8.0 cm separated by 2.0 mm of air. A slab of polystyrene (εᵣ = 2.6) exactly filling the gap is inserted. (a) Calculate the capacitance before and after insertion. (b) If the capacitor is charged to 12 V with the dielectric in place, find the energy stored.
Answer. C₀ ≈ 28.3 pF; C ≈ 73.6 pF; Energy stored ≈ 5.30 nJ
Origins · 1 minMichael Faraday and how this was discovered
Faraday coined the term 'dielectric' and conducted systematic experiments in the 1830s showing that the material between capacitor plates affects the capacitance. He introduced the concept of the electric field and field lines, and defined the specific inductive capacity — what we now call relative permittivity — by carefully comparing capacitors filled with different insulators. Faraday had almost no formal mathematical education yet revolutionised physics; James Clerk Maxwell later translated Faraday's physical intuitions into the rigorous mathematical framework of electromagnetism.
Related Concepts
- Electric Field and Field Lines — Polarisation is a direct response of bound charges to an applied electric field; understanding field lines helps visualise how the field changes inside a dielectric.
- Capacitors and Capacitance — The primary practical application of dielectrics is increasing capacitance; the formula C = εᵣε₀A/d directly links dielectric properties to capacitor behaviour.
- Conductors in Electrostatic Equilibrium — Understanding why dielectrics behave differently from conductors requires contrasting the free charges in metals with the bound charges in insulators.
- Electric Potential and Voltage — Inserting a dielectric at constant voltage reduces the electric field inside, while inserting it at constant charge increases the stored energy — both are analysed using electric potential.