Electric Susceptibility Explained: Definition, Formula, and Units

Electric susceptibility is a crucial property in physics that measures how easily a dielectric material can be polarized by an external electric field. This page details the definition, formula, unit, and relationship to the dielectric constant, offering clear explanations, derivations, and examples for students and exam preparation.

What is Electric Susceptibility? (Definition & Meaning)

Electric susceptibility, often represented by the symbol $\chi_e$ (electric susceptibility symbol), is a dimensionless quantity describing the extent to which a dielectric material (insulator) becomes polarized when placed in an electric field. In physics, the electric susceptibility definition would be: the ratio of polarization density ($\mathbf{P}$) induced in the material to the product of the vacuum permittivity ($\varepsilon_0$) and the applied electric field ($\mathbf{E}$).

When an external electric field is applied to a dielectric, the charges (positive and negative) within its molecules slightly shift, creating induced dipoles. The measure of how easily this polarization occurs is given by the material's electric susceptibility. Materials with a higher electric susceptibility polarize more efficiently under the same applied field.

Electric susceptibility in hindi: विद्युत अनुक्रियता एक भौतिक राशि है जो दर्शाती है कि कोई निर्बाध (डायइलेक्ट्रिक) पदार्थ बाहरी विद्युत क्षेत्र में कितना ध्रुवीकृत हो सकता है।

Electric Susceptibility and Dielectric Constant

Electric susceptibility and dielectric constant are closely linked concepts in the study of dielectric materials. The dielectric constant (also called relative permittivity, symbol $\varepsilon_r$) quantifies how much a material can “store” electric flux compared to a vacuum, while electric susceptibility measures how readily it can be polarized.

Their relationship is expressed by:

• $\varepsilon_r = 1 + \chi_e$
• Or, $\chi_e = \varepsilon_r - 1$

For example, in a vacuum, $\varepsilon_r = 1$ and thus $\chi_e = 0$, meaning there is no polarization. For materials like water, which have a high dielectric constant, the electric susceptibility is also significantly high. More details about the dielectric can be found on the dielectric material page.

Electric Susceptibility Formula, Symbol, and Units

The electric susceptibility formula describes how polarization density relates to the applied electric field and vacuum permittivity:

Electric Susceptibility General Formula: $\chi_e = \frac{P}{\varepsilon_0 E}$

Alternatively, the polarization in a material is given by:

Where:

• $\mathbf{P}$ = Polarization density [C/m²]
• $\varepsilon_0$ = Permittivity of free space ($8.854 \times 10^{-12}~\text{F/m}$)
• $\chi_e$ = Electric susceptibility (symbol name chi_e)
• $\mathbf{E}$ = Applied electric field [V/m]

Electric susceptibility units: It is a dimensionless quantity (unitless) because it is a ratio of similar units. This is also reflected in the electric susceptibility dimensional formula, which is dimensionless ($M^0L^0T^0A^0$).

Electric susceptibility is denoted by the symbol $\chi_e$. For a full listing of electric susceptibility symbol name and symbols in physics, refer to the physics symbols guide.

Step-by-Step: How to Derive the Relation Between Electric Susceptibility and Dielectric Constant

Let’s derive how electric susceptibility and dielectric constant are related, which is important for both theoretical understanding and exam preparation (electric susceptibility class 12 students take note):

1. Start with the relationship: $\mathbf{P} = \varepsilon_0 \chi_e \mathbf{E}$
2. Total electric displacement (D) is given by: $\mathbf{D} = \varepsilon_0 \mathbf{E} + \mathbf{P}$
3. Substitute $\mathbf{P}$: $\mathbf{D} = \varepsilon_0 \mathbf{E} + \varepsilon_0 \chi_e \mathbf{E} = \varepsilon_0 (1 + \chi_e) \mathbf{E}$
4. But, by definition, $\mathbf{D} = \varepsilon \mathbf{E}$, where $\varepsilon$ is the absolute permittivity.
5. Therefore, $\varepsilon \mathbf{E} = \varepsilon_0 (1 + \chi_e) \mathbf{E} \implies \varepsilon = \varepsilon_0 (1 + \chi_e)$
6. Relative permittivity (dielectric constant) is $\varepsilon_r = \frac{\varepsilon}{\varepsilon_0}$
7. Therefore, $\varepsilon_r = 1 + \chi_e$

Relation Formula: $\boxed{\varepsilon_r = 1 + \chi_e}$

Types of Dielectric Materials and Their Susceptibility

Dielectric materials are classified based on their molecular structure, which impacts their electric susceptibility:

• Polar dielectrics: Molecules have permanent dipole moments (e.g., water ($\ce{H2O}$)). In an electric field, these align easily; hence, electric susceptibility of water is relatively high.
• Non-polar dielectrics: No permanent dipole moments (e.g., nitrogen, oxygen). Only induced polarization occurs, so electric susceptibility is lower.

The electric susceptibility of air and the electric susceptibility of vacuum are especially important reference points: for vacuum, $\chi_e = 0$ by definition; for dry air, $\chi_e$ is very close to zero.

Examples and Applications of Electric Susceptibility

Understanding electric susceptibility in physics is vital in many real-world technologies:

• Capacitors: Inserting a dielectric with high susceptibility between the plates increases capacitance.
• Transformers: Liquid dielectrics (oils with specific electric susceptibility) provide electrical insulation and cooling.
• Semiconductor devices: Dielectrics impact the performance of transistors and integrated circuits.
• Insulation: Materials with low electric susceptibility are used to minimize unwanted polarization.

Learn more about dielectric and related effects in electric polarization and Faraday’s Law.

Summary Table: Electric Susceptibility, Dielectric Constant & Related Quantities

This table summarizes how electric susceptibility values are derived and compared across reference substances like air, water, and vacuum, highlighting the electric susceptibility formula and the electric susceptibility dimensional formula.

Electric Susceptibility Tensor and Advanced Concepts

In isotropic materials, electric susceptibility is a single number. However, in anisotropic materials (such as certain crystals), the property must be described using an electric susceptibility tensor—a $3\times3$ matrix that shows different polarization responses along different axes. Exploring tensor forms helps in advanced applications in solid-state physics and crystallography.

For more foundational equations in class 12 physics and advanced derivations, explore our section on class 12 physics formulas.

Conclusion: Why Electric Susceptibility Matters in Physics

Electric susceptibility serves as a bridge between microscopic molecular behavior and macroscopic electrical properties in materials. Its formula and unitless nature make it simple to compare different substances. Understanding electric susceptibility, dielectric constant, and related formulas is essential for physics students, engineers, and anyone interested in how materials interact with electric fields. Continue exploring topics like electric susceptibility, polarization, and dielectrics to build a strong foundation in electromagnetism.