What is relative permittivity?

Question

Examoogle · Accepted Answer

Ratio of actual permittivity to absolute permittivity

Explanation: Relative permittivity, also known as the dielectric constant, is defined as the ratio of the absolute permittivity of a material ($\epsilon$) to the permittivity of free space or vacuum ($\epsilon_0$). It is a dimensionless quantity that characterizes how much a material can resist the formation of an electric field within it.

Working Principle: When a dielectric material is placed in an electric field, the dipoles within the material align to oppose the external field, effectively reducing the net electric field intensity. The ratio $\epsilon_r = \frac{\epsilon}{\epsilon_0}$ quantifies this reduction capability relative to a vacuum, where the vacuum's permittivity is the base reference point.

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

Key Points: Relative permittivity is a dimensionless quantity.; The value of $\epsilon_r$ for a vacuum is exactly 1.; For all other materials, $\epsilon_r > 1$.; It directly dictates the capacitance of a parallel-plate capacitor: $C = \frac{\epsilon_0 \epsilon_r A}{d}$.

Advantages: Useful for comparing insulating properties of different materials.; Simplifies calculation of dielectric behavior in electrical circuits.

Disadvantages: Temperature dependent in many dielectric materials.; Frequency dependent (dispersion) in polar materials.

Applications: Selection of insulation materials for cables and transformers.; Design of PCB substrates and high-frequency microwave circuits.

Additional Info: The permittivity of free space $\epsilon_0$ is approximately $8.854 	imes 10^{-12} 	ext{ F/m}$.. Option A is incorrect because absolute permittivity has units (F/m), while relative permittivity is dimensionless.. Option C is the reciprocal of the definition.. Option D is incorrect as it ignores the comparison with the vacuum reference.

Answer: B is correct — Relative permittivity is the dimensionless ratio of the permittivity of a material to the permittivity of free space.

Exam Tip: In competitive exams, remember that relative permittivity ($\epsilon_r$) is always greater than or equal to 1 for all physical materials, with air being very close to 1.0006.

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