---
title: "Frequency dependence of polarizability"
subject: "Electrical Engineering Material"
chapter: 3
key: "semester_3/electrical_engineering_material:polarizability-frequency-dependence"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/polarizability-frequency-dependence
site: BCT Engineering
---

# Frequency dependence of polarizability

Electrical Engineering Material · Chapter 3: Dielectric Materials

- Asked in: 2079 Bhadra, 5 marks
- Video: [Frequency and temperature dependence of dielectric polarization | Dielectrics](https://www.youtube.com/watch?v=d7aEl0RjeF0) — Raheemsir jee Physics
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/polarizability-frequency-dependence
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-3

## Question

Graphically explain frequency dependency of polarizability.

## Short answer

Total polarizability and permittivity decrease stepwise as frequency rises because slower mechanisms cease to respond: space-charge drops out ~10^2–10^3 Hz, orientational (dipolar) at ~10^6–10^10 Hz, ionic at ~10^13 Hz, electronic at ~10^15 Hz (UV). At optical frequencies only electronic remains, so epsilon_r = n^2. Loss peaks occur near each relaxation or resonance frequency.

## Answer

The **total polarizability** of a dielectric is $\alpha = \alpha_e + \alpha_i + \alpha_d$ (+ $\alpha_{sc}$ interfacial). Each mechanism needs a certain time to respond. When the applied AC field changes faster than a mechanism can follow, that mechanism drops out, so $\alpha$ (and $\varepsilon_r$) falls in steps as frequency rises.

```text
 alpha (or er)
   ^
   |____
   |    \  interfacial (space charge)
   |     \_______
   |             \   orientational
   |              \________
   |                       \/\  ionic
   |                          \_______
   |                                  \/\ electronic
   |                                     \______
   +----+--------+--------+--------+-------> f (Hz)
       1e2     1e6-1e9   1e13    1e15
       power   radio/MW  infra-   UV/
       freq.             red      optical
```

#### Explanation of each region
1. **Interfacial (space-charge) polarization**: charges drift to grain boundaries and electrodes. Very slow; it follows the field only up to about $10^2$–$10^3$ Hz.
2. **Orientational (dipolar) polarization**: permanent dipoles rotate. Molecules have inertia and suffer collisions, so they follow the field up to about $10^{6}$–$10^{10}$ Hz (radio/microwave). Above this, $\alpha_d \to 0$.
3. **Ionic polarization**: positive and negative ions are displaced. Ions are heavy, so a resonance occurs at infrared frequencies (~$10^{13}$ Hz).
4. **Electronic polarization**: the light electron cloud shifts. It follows the field up to UV/optical frequencies (~$10^{15}$ Hz). Above that, nothing can respond and $\varepsilon_r \to 1$.

#### Key points
- Near the **relaxation** frequencies (interfacial and orientational), the fall is smooth and the dielectric loss ($\varepsilon_r''$) shows a peak.
- Near each **resonance** (ionic, electronic) there is a small rise then a sharp drop, also with a loss peak.
- At optical frequencies only electronic polarization remains, so $\varepsilon_r = n^2$ (n = refractive index). Example: water has $\varepsilon_r \approx 80$ at low frequency but $n^2 \approx 1.77$ at optical frequency, because dipolar polarization has dropped out.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why does alpha (and eps_r) fall in steps as frequency rises?
   A. Each mechanism drops out when the field changes faster than it can respond
   B. The field amplitude decreases
   C. The material heats up
   D. Dipoles multiply
   Answer: A. Slower mechanisms stop following the field first. (Key point: Stepwise fall)

2. Which mechanism persists to the highest frequency?
   A. Interfacial
   B. Orientational
   C. Ionic
   D. Electronic
   Answer: D. The light electron cloud follows up to UV (about 10^15 Hz). (Key point: Order of dropout)

3. Ionic polarization shows resonance around:
   A. 10^2 Hz
   B. 10^13 Hz (infrared)
   C. 10^9 Hz
   D. 10^15 Hz
   Answer: B. Ions are heavy, so their resonance lies in the infrared. (Key point: Ionic region)

4. At optical frequencies, eps_r equals:
   A. Its static value
   B. Zero
   C. n^2, since only electronic polarization remains
   D. Infinity
   Answer: C. Water has eps_r about 80 at low frequency but n^2 of about 1.77 optically because dipolar polarization has dropped out. (Key point: Optical permittivity)

## Related in Electrical Engineering Material

- [Si polarizability, local field and resonant frequency](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Asi-polarizability-resonant-frequency) — Electrical Engineering Material, chapter 3, asked 2×