Polarisation — Revision Notes

⚡ 30-Second Revision

Dielectric — Insulator that polarises in E-field.
Polarisation (P) — Net dipole moment per unit volume. Unit: $C/m^2$.
Polar Molecules — Permanent dipoles (e.g., $H_2O$). Align in E-field.
Non-polar Molecules — Induced dipoles (e.g., $CO_2$). Form in E-field.
Electric Susceptibility ($\chi_e$) — Material's ease of polarisation. $\vec{P} = \epsilon_0 \chi_e \vec{E}$.
Dielectric Constant (K) — Factor of E-field reduction. $K = 1 + \chi_e$. For vacuum, $K=1$.
Effect on E-field — $E = E_0/K$.
Effect on Capacitance — $C = K C_0$.
Constant V (Battery connected) — $V$ constant, $E$ constant, $C \uparrow K$, $Q \uparrow K$, $U \uparrow K$.
Constant Q (Battery disconnected) — $Q$ constant, $C \uparrow K$, $V \downarrow K$, $E \downarrow K$, $U \downarrow K$.

2-Minute Revision

Polarisation is the phenomenon where a dielectric material, an electrical insulator, responds to an external electric field by developing or aligning electric dipole moments. This occurs differently for polar molecules (which have permanent dipoles that align) and non-polar molecules (which form induced dipoles).

The collective effect is quantified by the polarisation vector $\vec{P}$, representing the net dipole moment per unit volume. This internal polarisation creates an opposing electric field within the dielectric, reducing the net electric field $E$ to $E_0/K$, where $E_0$ is the external field and $K$ is the dielectric constant.

$K$ is related to the electric susceptibility $\chi_e$ by $K = 1 + \chi_e$. The most significant application is in capacitors, where introducing a dielectric increases capacitance by a factor of $K$ ($C = KC_0$).

Remember the two crucial scenarios: if the capacitor is connected to a battery (constant voltage), $E$ and $V$ remain constant, while $Q$ and $U$ increase by $K$. If disconnected (constant charge), $Q$ remains constant, while $V$, $E$, and $U$ all decrease by $K$.

These relationships are frequently tested in NEET.

5-Minute Revision

Polarisation is the fundamental response of dielectric (insulating) materials to an external electric field. It involves the microscopic rearrangement of charges within the material's molecules. Non-polar molecules, like $CO_2$, initially have no permanent dipole moment; the external field induces one by separating their charge centers.

Polar molecules, like $H_2O$, possess permanent dipole moments that are randomly oriented in the absence of a field; the external field exerts a torque, causing them to partially align. In both cases, the result is a net electric dipole moment per unit volume, defined as the **polarisation vector $\vec{P}$** (unit $C/m^2$).

This internal polarisation creates an electric field $\vec{E}_p$ within the dielectric that opposes the external applied field $\vec{E}_0$. Consequently, the net electric field $\vec{E}$ inside the dielectric is reduced: $\vec{E} = \vec{E}_0 - \vec{E}_p$.

The extent of this reduction is quantified by the **dielectric constant $K$** (or relative permittivity $\epsilon_r$), such that $E = E_0/K$. $K$ is a dimensionless quantity, always $K \ge 1$ (for vacuum, $K=1$).

The material's ability to polarise is also described by its **electric susceptibility $\chi_e$**, related to $K$ by $K = 1 + \chi_e$. The polarisation vector is also related to the net field by $\vec{P} = \epsilon_0 \chi_e \vec{E}$.

The most important application of polarisation in NEET is its effect on capacitors. When a dielectric of constant $K$ completely fills a capacitor, its capacitance increases by a factor of $K$: $C = K C_0$.

Key Scenarios for Capacitors with Dielectrics:

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Connected to a battery (Constant Voltage $V$) — The battery maintains a constant potential difference. Thus, $V = \text{constant}$.

* Electric Field $E = V/d$: Remains constant. * Capacitance $C = K C_0$: Increases by $K$. * Charge $Q = CV$: Increases by $K$ ($Q = K Q_0$). * Energy Stored $U = \frac{1}{2}CV^2$: Increases by $K$ ($U = K U_0$).

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Disconnected from a battery (Constant Charge $Q$) — The charge on the plates remains isolated.

* Charge $Q$: Remains constant. * Capacitance $C = K C_0$: Increases by $K$. * Potential Difference $V = Q/C$: Decreases by $K$ ($V = V_0/K$). * Electric Field $E = V/d$: Decreases by $K$ ($E = E_0/K$). * Energy Stored $U = Q^2/(2C)$: Decreases by $K$ ($U = U_0/K$).

Understanding these two scenarios and the underlying formulas is critical for NEET success.

Prelims Revision Notes

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Dielectrics — Insulating materials that can be polarised by an external electric field. They do not conduct electricity but allow charge displacement.
2
Polarisation — The process where molecular dipoles within a dielectric either align (polar molecules) or are induced (non-polar molecules) in the direction of an external electric field.
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Polar Molecules — Possess permanent electric dipole moments due to asymmetric charge distribution (e.g., $H_2O$, $HCl$). In an E-field, they experience torque and align.
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Non-polar Molecules — Have no permanent electric dipole moment; centers of positive and negative charge coincide (e.g., $O_2$, $CO_2$). In an E-field, dipoles are induced by charge separation.
5
Polarisation Vector ($\vec{P}$) — Net electric dipole moment per unit volume. Unit: $C/m^2$. It is related to the induced surface charge density $\sigma_p$ by $P = \sigma_p$.
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Electric Susceptibility ($\chi_e$) — Dimensionless constant indicating how easily a material polarises. $\vec{P} = \epsilon_0 \chi_e \vec{E}$. For vacuum, $\chi_e = 0$.
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Dielectric Constant (K or $\epsilon_r$) — Dimensionless factor by which the electric field is reduced and capacitance is increased. $K = 1 + \chi_e$. Always $K \ge 1$.
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Effect on Electric Field — The net electric field inside a dielectric $E = E_0/K$, where $E_0$ is the external field. The internal field due to polarisation opposes $E_0$.
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Effect on Capacitance — When a dielectric fills a capacitor, its capacitance increases: $C = K C_0$, where $C_0$ is the capacitance in vacuum.
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Capacitor Scenarios (Crucial for NEET)

* **Connected to Battery (Constant Voltage $V$)**: $V$ constant, $E$ constant, $C \uparrow K$, $Q \uparrow K$, $U \uparrow K$. * **Disconnected from Battery (Constant Charge $Q$)**: $Q$ constant, $C \uparrow K$, $V \downarrow K$, $E \downarrow K$, $U \downarrow K$.

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Energy Stored — $U = \frac{1}{2}CV^2 = \frac{Q^2}{2C}$. Apply $K$ correctly based on the scenario.
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Dielectric Strength — Maximum electric field a dielectric can withstand before breakdown (becoming conductive).

Vyyuha Quick Recall

Polarization Decreases Electric Field, Increases Capacitance.

Polar Molecules Align, Non-polar Molecules Induce.

K = 1 + Chi-E (K is 1 plus susceptibility).

Constant Voltage: Charge, Capacitance, U (Energy) Increase. Constant Q (Charge): Voltage, Electric Field, U (Energy) Decrease.