Dielectrics in Capacitors
A capacitor stores electric charge by maintaining an electric field between two conducting plates separated by a gap. When that gap is filled with an insulating material — called a dielectric — something remarkable happens: the capacitor can store significantly more charge for the same applied voltage. This effect is not a trick of engineering; it arises from the fundamental physics of how electric fields interact with matter at the molecular level. Every insulating material has a property called its dielectric constant (or relative permittivity), denoted κ (kappa), which is always greater than or equal to 1. When a dielectric slab is inserted between the plates of a capacitor, the capacitance increases by a factor of κ. Simultaneously, the electric field inside the capacitor is reduced by the same factor κ. These two facts — more capacitance, weaker field — are two sides of the same coin, and understanding why requires exploring how molecules respond to electric fields. Dielectrics are used in virtually every real capacitor you will ever encounter, from the tiny surface-mount components on a circuit board to the large capacitors in power supplies. They serve a dual purpose: increasing capacitance (allowing smaller physical devices) and acting as a physical separator that prevents the plates from touching and short-circuiting. Materials like mica, ceramic, paper, and certain polymers are chosen for their high dielectric constants, low energy loss, and ability to withstand high voltages.
- Polarisation of Molecules
- Bound Surface Charges
- The Induced Field Opposes the Applied Field
- Capacitance Increases by Factor κ
- Energy Considerations
Polarisation of Molecules
Atoms and molecules in an insulator have no free electrons — they cannot conduct. However, when placed in an electric field, the electron clouds in each molecule shift slightly toward the positive plate, while the positive nuclei shift slightly toward the negative plate. This separation of charge within each molecule creates a tiny electric dipole. The material becomes polarised: billions of aligned dipoles throughout the slab.
Bound Surface Charges
The aligned dipoles produce what are called bound charges on the surfaces of the dielectric. The surface facing the positive plate acquires a net negative bound charge, and the surface facing the negative plate acquires a net positive bound charge. These bound charges are NOT free to move — they remain anchored to their molecules. Think of it like a crowd of people each leaning in the same direction: no one has moved away, but the crowd has shifted.
The Induced Field Opposes the Applied Field
The bound surface charges create their own electric field, E_induced, that points opposite to the original field E_0 set up by the free charges on the plates. The net electric field inside the dielectric is therefore E = E_0 − E_induced = E_0 / κ, where κ ≥ 1. The field is weakened inside the material. If you connect a battery, the battery pushes more free charge onto the plates to compensate, raising the charge stored Q for the same voltage V.
Capacitance Increases by Factor κ
Capacitance is defined as C = Q/V. With a dielectric, for the same voltage V the plates hold more charge Q (because the weakened field means the battery must deliver more charge to maintain the same potential difference). The result is C = κC_0, where C_0 is the capacitance without the dielectric (in a vacuum or air). This factor κ — the relative permittivity — is a property of the material: for air κ ≈ 1, for paper κ ≈ 3.5, for water κ ≈ 80, for some ceramics κ > 10,000.
Energy Considerations
If a dielectric is inserted into an isolated capacitor (disconnected from a battery), charge Q is fixed. Since C increases, and energy stored is U = Q²/(2C), the energy actually decreases — energy is released as the dielectric is pulled in, which is why a dielectric slab is spontaneously attracted into the gap between charged plates. If instead the capacitor stays connected to a battery (fixed V), the energy stored U = ½CV² increases as C increases, but the battery must supply extra energy to push the additional charge onto the plates.
The Key Equation
- C — Capacitance (Farads (F)): The ability of the capacitor to store charge per unit voltage.
- \kappa — Dielectric constant (relative permittivity) (Dimensionless): A material property ≥ 1 indicating how much the capacitance increases relative to vacuum.
- \varepsilon_0 — Permittivity of free space (F/m): The fundamental constant 8.85 × 10⁻¹² F/m describing how well a vacuum permits electric fields.
- A — Plate area (m²): The overlapping area of the two conducting plates.
- d — Plate separation (m): The distance between the two plates, entirely filled by the dielectric.
Worked Example
Problem. A parallel-plate capacitor has square plates of side 8.0 cm separated by a 2.0 mm air gap. (a) Find the capacitance C₀. (b) A mica slab (κ = 5.4) exactly fills the gap. Find the new capacitance C. (c) If the capacitor is connected to a 12 V battery with the mica in place, find the charge stored Q and the electric field E inside the mica.
Answer. C₀ ≈ 28.3 pF; C (with mica) ≈ 153 pF; Q ≈ 1.83 nC; E = 6000 V/m inside the mica.
Origins · 1 minMichael Faraday and how this was discovered
Faraday coined the term 'dielectric' and conducted pioneering experiments in the 1830s showing that the material between capacitor plates affects capacitance. He systematically measured the capacitance of Leyden jars filled with different insulators, discovering that the stored charge depended on the medium — a revolutionary finding that challenged the prevailing view that only the geometry mattered. He also introduced the concept of electric field lines and permittivity. Faraday had almost no formal mathematical education; he left school at 14 to work as a bookbinder's apprentice. Despite this, he became one of the greatest experimental physicists in history, and James Clerk Maxwell later translated his physical intuitions into the full mathematical theory of electromagnetism.
Related Concepts
- Capacitance of a Parallel-Plate Capacitor — Dielectrics modify the fundamental formula C = ε₀A/d by introducing the factor κ; understanding the base formula is essential before adding the dielectric.
- Electric Field and Electric Potential — The dielectric reduces the electric field inside by 1/κ; this directly affects the potential difference and the relationship E = V/d.
- Energy Stored in a Capacitor — Inserting a dielectric changes the stored energy U = Q²/2C or U = ½CV²; understanding which quantity is held constant (Q or V) determines whether energy increases or decreases.
- Electric Dipoles and Polarisation — The microscopic mechanism behind dielectrics is molecular polarisation — the alignment of dipoles in response to an external field.