8 min readConcept sheet2 or 3-mark questions on polar and non-polar molecules and how a dielectric reduces a field, and 1-mark MCQ on dielectric constant

Dielectrics and electric polarisation

A dielectric has no free charges. In a field its molecules become lined-up dipoles, and the surface charges they create reduce the field inside to E₀/K.

Polarisation PDipole moment per unit volume, unit C m⁻²; P = ε₀χₑE for a linear isotropic dielectric (χₑ is the electric susceptibility)

Dielectric constantK = ε/ε₀ = C/C₀; also called relative permittivity (εᵣ); K > 1 for every dielectric

Field inside a dielectric slabE = E₀/K, where E₀ is the applied field

Induced surface chargeBound charge densities −σₚ and +σₚ: negative on the face where the field enters, positive where it leaves

Non-polar vs polar molecules

Non-polar moleculesThe centres of positive and negative charge coincide, so there is no permanent dipole moment. Examples: O₂, H₂, N₂. In a field, the charges shift apart a little, giving an induced dipole along the field.

Polar moleculesThe centres of positive and negative charge are separated, so each molecule has a permanent dipole moment. Examples: H₂O, HCl. Without a field the dipoles point randomly and cancel. A field turns them partly into line; thermal motion resists this.

Either way, a dielectric in a field gains a net dipole moment along the field. This is polarisation.

How a dielectric slab reduces the field

Place a dielectric slab in a uniform external field E₀, at right angles to its faces.

1
Each molecule becomes a dipole lined up with E₀ (induced, or turned into line).
2
Inside the slab, the + end of one dipole sits next to the − end of the next, so there is no net charge in the bulk.
3
At the faces, the ends are left uncovered: negative charge on the face where the field enters, positive charge on the face where it leaves.
4
These surface charges make a field opposite to E₀ inside the slab.
5★
So the net field inside is reduced: E = E₀/K. It is not zero, because bound charges can shift only a little.

★ key step

Conductor vs dielectric in an external field

ConductorFree charges move all the way to the surfaces. Their field exactly cancels the outside field, so E = 0 inside. (K is effectively infinite.)

DielectricBound charges shift only slightly. Their field partly cancels the outside field, so E = E₀/K inside: smaller, but not zero.

Dielectric constants (approximate)

Material	K
Vacuum	1 (exactly)
Air	about 1.0006, taken as 1
Glass	about 5 to 10
Mica	about 6
Water	about 80

Polarisation and permittivity

Polarisation P is the dipole moment per unit volume, so its unit is C m⁻². For most materials (linear and isotropic), P is proportional to the field: P = ε₀χₑE. The constant χₑ, which has no unit, is the electric susceptibility. The permittivity of the medium is ε = ε₀K, so the dielectric constant is K = ε/ε₀. Because a dielectric weakens fields, it weakens the Coulomb force between charges K times. It also raises the capacitance of a capacitor K times. Extra help, beyond your textbook: K = 1 + χₑ.

Worked example: field inside a slab

Problem

A uniform field of 6 × 10⁴ N C⁻¹ acts at right angles to a glass slab of dielectric constant 6. Find (a) the field inside the slab and (b) the potential difference across the slab if it is 5 mm thick.

Working

(a) E = E₀/K = 6 × 10⁴ ÷ 6 = 1 × 10⁴ N C⁻¹.
(b) The field inside is uniform, so V = Ed = 1 × 10⁴ N C⁻¹ × 5 × 10⁻³ m = 50 V.

Answer

(a) 1 × 10⁴ N C⁻¹; (b) 50 V

In real life

Water's dielectric constant is about 80, so it weakens the pull between Na⁺ and Cl⁻ ions about 80 times. That is why salt dissolves easily in water for your sambar, but not in cooking oil, whose dielectric constant is small.

Exam angle

2 marks: “Distinguish between polar and non-polar molecules, giving one example of each.” Polar: centres of + and − charge separated, so a permanent dipole (H₂O). Non-polar: centres coincide, so no permanent dipole (O₂). Both get polarised in a field.

3 marks: “Explain, with a labelled diagram, how a dielectric slab placed in a uniform field reduces the field inside it. Define dielectric constant.” Molecules line up as dipoles; charges cancel in the bulk; −σₚ and +σₚ appear on the faces; their field opposes E₀, so E = E₀/K. K = ε/ε₀ = E₀/E.

1 marks: “What is the dielectric constant of a metal?” Effectively infinite, because the field inside a conductor is zero.

Remember it

Polar = permanent dipole (water); non-polar = no dipole until a field acts (oxygen). A dielectric divides the field by K.