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Physics · Electrostatic Potential and Capacitance

Dielectrics and Polarisation

A dielectric is a non-conducting substance that responds to an external field not by conducting charge but by polarising. NCERT Section 2.10 develops this idea from the molecular level upward, and it is the conceptual hinge on which the entire dielectric-on-capacitance result later turns. For NEET, this subtopic supplies a steady stream of single-line conceptual questions on polar molecules, induced dipoles and the reduced internal field.

What Is a Dielectric

Dielectrics are non-conducting substances. In contrast to conductors, they have no (or a negligible number of) charge carriers. Recall the behaviour of a conductor placed in an external field: its free charge carriers move, and the charge distribution rearranges itself so that the field due to the induced charges opposes the external field within the conductor. This continues until, in the static situation, the two fields cancel exactly and the net electrostatic field inside the conductor is zero.

In a dielectric, this free movement of charges is not possible. Instead, the external field induces a dipole moment by stretching or re-orienting the molecules of the dielectric. The collective effect of all the molecular dipole moments is a net charge on the surface of the dielectric, which produces a field that opposes the external field. Unlike in a conductor, however, the opposing field so induced does not exactly cancel the external field — it only reduces it. The extent of the effect depends on the nature of the dielectric.

Figure 1 · Conductor vs Dielectric External field E₀ → Conductor − + E = 0 field fully cancelled Dielectric − + E = E₀ / K field only reduced

A conductor screens the field to zero; a dielectric, whose charges are bound, only weakens it to $E_0/K$.

Polar vs Non-Polar Molecules

To understand the effect, we look at the charge distribution of a dielectric at the molecular level. The molecules of a substance may be polar or non-polar. In a non-polar molecule, the centres of positive and negative charges coincide, so the molecule has no permanent (or intrinsic) dipole moment. Oxygen ($\mathrm{O_2}$) and hydrogen ($\mathrm{H_2}$), because of their symmetry, are examples. In a polar molecule, the centres of positive and negative charges are separated even when there is no external field, so such molecules carry a permanent dipole moment. An ionic molecule such as HCl, or a molecule of water ($\mathrm{H_2O}$), are examples.

Figure 2 · Molecular charge distribution Non-polar (e.g. O₂, H₂) + , − coincide no permanent dipole · p = 0 Polar (e.g. HCl, H₂O) − + p permanent dipole · p ≠ 0

In a non-polar molecule the two charge centres sit on top of one another; in a polar molecule they are permanently displaced.

FeatureNon-polar moleculePolar molecule
Charge centresCoincidePermanently separated
Dipole moment with no fieldZeroPermanent, non-zero
Origin of net moment in fieldInduced by displacement of chargesAlignment of permanent dipoles
Temperature dependenceWeakAlignment competes with thermal agitation
Examples$\mathrm{O_2}$, $\mathrm{H_2}$HCl, $\mathrm{H_2O}$

How Polarisation Arises

In an external field, the positive and negative charges of a non-polar molecule are displaced in opposite directions. The displacement stops when the external force on the constituent charges is balanced by the restoring force due to internal fields in the molecule. The non-polar molecule thus develops an induced dipole moment, and the dielectric is said to be polarised. We consider only the simple case where the induced dipole moment is in the direction of the field and is proportional to the field strength — substances obeying this are called linear isotropic dielectrics. The induced dipole moments of different molecules add up, giving a net dipole moment of the dielectric.

A dielectric with polar molecules also develops a net dipole moment in an external field, but for a different reason. In the absence of any external field, the permanent dipoles are oriented randomly due to thermal agitation, so the total dipole moment is zero. When a field is applied, the individual moments tend to align with it; summed over all molecules, there is a net dipole moment in the direction of the field. The extent of polarisation depends on two opposing factors: the dipole potential energy in the field, which tends to align the dipoles, and the thermal energy, which tends to disrupt the alignment. There may also be an induced-dipole contribution as for non-polar molecules, but the alignment effect is generally more important for polar molecules.

Thus in either case, whether polar or non-polar, a dielectric develops a net dipole moment in the presence of an external field.

NEET Trap

Permanent dipole is the hallmark of a polar molecule

NEET phrases this as a definition question. A polar molecule is defined by a permanent dipole moment that exists even with no external field — not one that appears only when the field is switched on. The "acquires a dipole only in a field" option describes a non-polar molecule.

Permanent dipole, no field needed = polar. Induced dipole, only in a field = non-polar.

The Polarisation Vector P

The dipole moment per unit volume is called the polarisation and is denoted by $\mathbf{P}$. For linear isotropic dielectrics, the polarisation is directly proportional to the field that produces it:

$$\mathbf{P} = \varepsilon_0\, \chi_e\, \mathbf{E}$$

where $\chi_e$ is a constant characteristic of the dielectric, known as the electric susceptibility of the medium. A larger $\chi_e$ means the substance polarises more strongly for the same field, and it is possible to relate $\chi_e$ to the molecular properties of the substance. The proportionality of $\mathbf{P}$ to $\mathbf{E}$ is precisely what makes the dielectric's effect on the field — and hence on capacitance — a constant multiplicative factor.

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Where this leads

The reduced internal field is exactly why a dielectric raises capacitance. See it worked out in Effect of a Dielectric on Capacitance.

Bound Surface Charges and the Reduced Field

How does the polarised dielectric modify the original external field inside it? Consider a rectangular dielectric slab placed in a uniform external field $\mathbf{E_0}$ parallel to two of its faces. The field causes a uniform polarisation $\mathbf{P}$ of the dielectric, so every volume element $\Delta v$ of the slab has a dipole moment $\mathbf{P}\,\Delta v$ in the direction of the field. Such a volume element is macroscopically small but contains a very large number of molecular dipoles.

Anywhere inside the dielectric, a volume element has no net charge, even though it has a net dipole moment, because the positive charge of one dipole sits close to the negative charge of the adjacent dipole. However, at the surfaces normal to the field there is a net charge density: the positive ends of the dipoles remain unneutralised at the right surface and the negative ends at the left surface. These unbalanced charges are the induced charges due to the external field.

Figure 3 · Polarised slab in a uniform field External field E₀ −σₚ +σₚ bound surface charges (not free) E = E₀/K

Inside the slab the dipoles leave no net charge, but the surfaces carry $\pm\sigma_p$. The field of these surface charges opposes $\mathbf{E_0}$, reducing the net field to $E_0/K$.

Thus, the polarised dielectric is equivalent to two charged surfaces with induced surface charge densities, say $+\sigma_p$ and $-\sigma_p$. The field produced by these surface charges opposes the external field, so the total field in the dielectric is reduced from the case when no dielectric is present. Crucially, the surface charge density $\pm\sigma_p$ arises from bound charges, not free charges: they cannot be drawn off as conduction current and exist only because the molecular dipoles are anchored in place.

NEET Trap

Bound surface charge is not free charge

The induced $\pm\sigma_p$ on a dielectric surface looks like the charge on a conductor plate, but it is bound charge. It cannot move through the material and it does not fully cancel the external field. This is why the field inside a dielectric falls only to $E_0/K$ and never reaches zero — unlike inside a conductor, where free charge cancels the field completely.

Conductor: free charge, net field = 0. Dielectric: bound charge, net field = $E_0/K$.

Dielectric Constant K

The factor by which the dielectric weakens the field is the dielectric constant $K$, also written as the relative permittivity $\varepsilon_r$. As NIOS Section 16.3.3 states, it is the ratio of the permittivity of the medium to the permittivity of free space:

$$K = \varepsilon_r = \frac{\varepsilon}{\varepsilon_0}$$

Equivalently, $K$ is the ratio of the electrostatic force between two point charges held a fixed distance apart in vacuum to the force between them at the same distance in the medium. The same constant reappears as the ratio of the capacitance with the dielectric between the plates to the capacitance with vacuum, $K = C_m/C_0$, so that $C_m = K C_0$. For metals $K = \infty$, for mica $K \approx 6$, and for paper $K = 3.6$.

QuantitySymbolDefining relation / value
Polarisation$\mathbf{P}$$\mathbf{P}=\varepsilon_0\chi_e\mathbf{E}$ — dipole moment per unit volume
Electric susceptibility$\chi_e$Characteristic of the medium; larger means stronger polarisation
Bound surface charge density$\pm\sigma_p$On faces normal to the field; from bound charge
Reduced internal field$E$$E = E_0/K$
Dielectric constant$K=\varepsilon_r$$\varepsilon/\varepsilon_0$; mica $\approx 6$, paper $=3.6$, metal $=\infty$
Quick Recap

Dielectrics and Polarisation in one screen

  • A dielectric is a non-conductor; in a field its molecules acquire dipole moments rather than conducting charge.
  • Non-polar molecules ($\mathrm{O_2}$, $\mathrm{H_2}$): charge centres coincide, no permanent dipole, an induced dipole appears in a field.
  • Polar molecules (HCl, $\mathrm{H_2O}$): permanent dipole exists with no field; the field aligns the random dipoles.
  • Polarisation $\mathbf{P}$ = dipole moment per unit volume; for linear dielectrics $\mathbf{P}=\varepsilon_0\chi_e\mathbf{E}$.
  • Polarisation leaves bound surface charges $\pm\sigma_p$ whose field opposes $\mathbf{E_0}$, reducing the net field to $E_0/K$ (not to zero).
  • The dielectric constant $K=\varepsilon_r=\varepsilon/\varepsilon_0$ is also $C_m/C_0$ — the bridge to the dielectric's effect on capacitance.

NEET PYQ Snapshot — Dielectrics and Polarisation

Conceptual recall on polar molecules and on relating the dielectric constant to permittivity.

NEET 2021

Polar molecules are the molecules

  1. Having a permanent electric dipole moment
  2. Having zero dipole moment
  3. Acquire a dipole moment only in the presence of electric field due to displacement of charges
  4. Acquire a dipole moment only when magnetic field is absent
Answer: (1)

In polar molecules the centre of positive charges does not coincide with the centre of negative charges, so these molecules have a permanent electric dipole moment of their own. Option (3) describes a non-polar molecule.

NEET 2020

The capacitance of a parallel plate capacitor with air as medium is 6 µF. With the introduction of a dielectric medium, the capacitance becomes 30 µF. The permittivity of the medium is ($\varepsilon_0 = 8.85\times10^{-12}\ \mathrm{C^2 N^{-1} m^{-2}}$):

  1. $1.77\times10^{-12}\ \mathrm{C^2 N^{-1} m^{-2}}$
  2. $0.44\times10^{-10}\ \mathrm{C^2 N^{-1} m^{-2}}$
  3. $5.00\ \mathrm{C^2 N^{-1} m^{-2}}$
  4. $0.44\times10^{-13}\ \mathrm{C^2 N^{-1} m^{-2}}$
Answer: (2)

Since $C_m = \varepsilon_r C_0$, the dielectric constant is $\varepsilon_r = 30/6 = 5$. The permittivity of the medium is $\varepsilon = \varepsilon_0\varepsilon_r = 8.85\times10^{-12}\times5 = 0.44\times10^{-10}\ \mathrm{C^2 N^{-1} m^{-2}}$.

FAQs — Dielectrics and Polarisation

The recurring conceptual snags NEET likes to test on this subtopic.

What is the difference between a polar and a non-polar molecule?

In a non-polar molecule the centres of positive and negative charge coincide, so it has no permanent dipole moment; oxygen and hydrogen are examples. In a polar molecule the centres of positive and negative charge are separated even with no external field, so it carries a permanent dipole moment; HCl and water are examples.

Why does the net field inside a dielectric reduce instead of becoming zero?

Charges in a dielectric are bound, not free, so they cannot fully migrate as in a conductor. The induced bound surface charges produce an opposing field that only partially cancels the external field. The net field is reduced to E0/K rather than to zero, where K is the dielectric constant.

What is polarisation P of a dielectric?

Polarisation P is the net dipole moment per unit volume induced in a dielectric by an external field. For linear isotropic dielectrics P is proportional to the field, P = epsilon0 * chi_e * E, where chi_e is the electric susceptibility of the medium.

What is the dielectric constant K?

The dielectric constant K, also called relative permittivity epsilon_r, is the ratio of the permittivity of the medium to the permittivity of free space, epsilon_r = epsilon/epsilon0. It equals the factor by which a dielectric increases the capacitance of a parallel plate capacitor, Cm = K*C0, and the factor by which it reduces the field inside, E = E0/K.

Are the induced surface charges on a dielectric free charges?

No. The induced surface charge densities plus or minus sigma_p arise from bound charges, not free charges. They appear on the surfaces normal to the field because the positive ends of dipoles remain unneutralised at one surface and the negative ends at the other; they cannot be drawn off as conduction charge.

Do polar dielectrics polarise differently from non-polar ones?

Yes. A non-polar molecule develops an induced dipole moment because the external field displaces its positive and negative charges. A polar molecule already has a permanent dipole; the field aligns these randomly oriented dipoles. In both cases the dielectric ends up with a net dipole moment along the field.

Related Topics
Electrostatic Potential and Capacitance Back to the full chapter hub. Electrostatics of Conductors Why free charge cancels the field to zero — the contrast case. Dielectric on Capacitance How the reduced field raises capacitance by K. Parallel Plate Capacitor The geometry where dielectrics are inserted. Capacitors and Capacitance The defining relation C = Q/V. Potential Due to a Dipole The dipole that every polarised molecule becomes.