9 min readConcept sheetSection A objective parts (polar or non-polar, true or false); Section B very short answer (2 marks) on polarisation, or short answer (3 marks) on a dielectric slab in a capacitor; also a NEET favourite

Dielectrics, polarisation and their effect on capacitance

In a field, a dielectric's molecules line up as tiny dipoles. Their field opposes E, so V falls and C rises K times: C = KC₀.

DielectricAn insulator that passes on electric effects without conducting; for example mica, paper, glass and oil

Non-polar and polarNon-polar (N₂, O₂, CO₂, methane, benzene): no permanent dipole. Polar (H₂O, NH₃, HCl): a permanent dipole

Dielectric constant KK = ε/ε₀ = F(vacuum)/F(medium) = C(medium)/C(vacuum); paper about 3.6, mica about 6, metals infinite

Field in a polarised slabE(effective) = E − Eₚ, smaller than the applied field E

Non-polar vs polar dielectrics

Non-polar dielectricsIn each molecule the centres of positive and negative charge coincide, so there is no permanent dipole moment. The molecules are usually symmetrical: N₂, O₂, CO₂, methane, benzene. A field pulls the charge centres apart, giving each molecule an induced dipole p = αε₀E, where α is its polarisability.

Polar dielectricsThe molecules are not symmetrical, so the charge centres are apart: each has a permanent dipole moment. Examples: water, NH₃, HCl. Without a field the dipoles point every way and cancel. A field turns them partly into line with it.

Either way, in a field the dielectric gains a net dipole moment along the field. It is then said to be polarised.

How a dielectric slab raises the capacitance

A slab of non-polar dielectric is placed between the plates of a charged capacitor, where the field is E.

1
In each molecule the nuclei are pushed towards the negative plate and the electrons towards the positive plate.
2
Each molecule becomes a tiny dipole. Inside the slab, the + end of one sits next to the − end of the next, so they cancel.
3
At the faces they do not cancel: a layer of negative charge faces the + plate, and a layer of positive charge faces the − plate.
4
These layers set up a field Eₚ opposite to E. The effective field E − Eₚ is smaller than before.
5
With the same charge on the plates, the potential difference V = Ed falls.
6★
So, C = q/V rises. If the slab fills the gap, C = KC₀.

★ key step

Three ways to define the dielectric constant

The dielectric constant K, also called the relative permittivity εᵣ, has no unit. (1) K = ε/ε₀: the permittivity of the medium divided by that of free space. (2) K = F(vacuum)/F(medium): the force between two charges at a fixed distance is K times smaller in the medium. (3) K = C(with dielectric)/C(with vacuum): filling the gap raises the capacitance K times. K is more than 1 for every dielectric. Typical values: paper about 3.6 and mica about 6. For a metal, K is taken as infinite.

Putting in a dielectric slab: battery joined or removed

Quantity	Battery stays connected (V fixed)	Battery removed first (Q fixed)
Capacitance	Becomes KC₀	Becomes KC₀
Charge	Becomes KQ₀	Stays Q₀
Potential difference	Stays V₀	Becomes V₀/K
Field between the plates	Stays E₀	Becomes E₀/K
Energy stored	Becomes KU₀	Becomes U₀/K

Worked example: a slab that fills half the gap

Problem

A parallel plate air capacitor has C₀ = 12 μF. A dielectric slab of K = 3, with the same area as the plates, fills half the gap. Find the new capacitance.

Working

Treat it as two capacitors in series, each with a gap of d/2: one filled with air, one with the slab.
Air part: C₂ = ε₀A/(d/2) = 2C₀ = 24 μF.
Slab part: C₁ = Kε₀A/(d/2) = 2KC₀ = 2 × 3 × 12 = 72 μF.
In series: C = C₁C₂/(C₁ + C₂) = 72 × 24 ÷ (72 + 24) = 1728 ÷ 96 = 18 μF.
Check with the shortcut C = 2KC₀/(K + 1) = 2 × 3 × 12 ÷ 4 = 18 μF.

Answer

18 μF: more than C₀, but less than 3C₀ = 36 μF, because the slab fills only half the gap

How to draw a polarised dielectric slab

Draw two vertical plates, with + signs on the left plate and − signs on the right plate.
Shade a slab between them. Inside it, draw a few small ovals, each marked − at its left end and + at its right end.
Mark a row of − signs on the left face of the slab and a row of + signs on its right face.
Draw a long arrow E from left to right between the plates, and a shorter arrow Eₚ from right to left inside the slab.

In real life

Waxed paper, mica and plastic films act as the dielectric inside the capacitors of fans, radios and phone chargers. Water's large dielectric constant, about 80, weakens the pull between ions, which helps salt dissolve in it.

Exam angle

1 marks: “Name one polar and one non-polar dielectric.” Polar: water (or NH₃, HCl). Non-polar: N₂ (or O₂, CO₂, methane, benzene).

2 marks: “A capacitor is charged and the battery is removed. A dielectric slab is then pushed in to fill the gap. What happens to its charge, its potential difference and its capacitance?” The charge stays the same, as it has nowhere to go. The field and the potential difference fall K times. The capacitance rises K times.

3 marks: “Explain, with a diagram, how a non-polar dielectric placed in a capacitor increases its capacitance.” The molecules become induced dipoles; negative charge appears on the slab face near the + plate and positive charge near the − plate; their field Eₚ opposes E, so E(effective) = E − Eₚ. V = Ed falls, so C = q/V rises (C = KC₀ if the gap is filled). Draw the polarised slab.

Remember it

Polar molecules are born dipoles, non-polar ones are made dipoles. Either way the slab fights the field, so V drops and C climbs.