What is the unit for relative permittivity?

Question

Examoogle · Accepted Answer

No unit

Explanation: Relative permittivity (also known as dielectric constant) is a dimensionless ratio that measures the ability of a material to store electrical energy in an electric field. Because it is defined as the ratio of the permittivity of a material to the permittivity of free space, the units cancel out, leaving it as a pure scalar quantity.

Working Principle: Relative permittivity is expressed as $\epsilon_r = \frac{\epsilon}{\epsilon_0}$. Here, $\epsilon$ is the absolute permittivity of the dielectric medium and $\epsilon_0$ is the permittivity of free space (vacuum), both measured in Farads per meter (F/m). Since it represents the factor by which the capacitance of a capacitor increases when a dielectric is inserted, it serves as a comparative index rather than an absolute measurement.

Key Formulas: $\epsilon_r = \frac{\epsilon}{\epsilon_0}$ — Definition of relative permittivity; $\epsilon = \epsilon_0 \cdot \epsilon_r$ — Relation between absolute and relative permittivity

Key Points: Relative permittivity is always greater than or equal to 1 for all materials.; It is a fundamental property for designing capacitors and insulating materials.; The value $\epsilon_0$ is approximately $8.854 	imes 10^{-12}$ F/m.; Being a ratio, it has no units, making it a dimensionless quantity.

Advantages: Simplifies calculations in electromagnetism.; Provides a standardized way to compare dielectric materials.

Applications: Design of high-frequency transmission lines.; Selection of dielectric materials for capacitor construction.; Material science research for insulators.

Additional Info: Vacuum has a relative permittivity of exactly 1.. Option A (F/m) is the unit for absolute permittivity ($\epsilon$).. Option B (Fm) is dimensionally incorrect.. Option C (F/m^2) is dimensionally incorrect.

Answer: D is correct — Relative permittivity is a dimensionless ratio of two quantities having the same units, and therefore has no unit.

Exam Tip: Always verify if a quantity is an absolute physical property (usually has units) or a ratio/coefficient (often dimensionless) in electrical engineering exams.

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