Electric Fields and Charges: Permittivity & Relative Permittivity

Introduction

Topic: Permittivity & Relative Permittivity
Build-up from Coulomb's Law
Importance of permittivity in different media
Scope: board level discussions, numerical problems at board and competitive exams level

Coulomb's Law: Force (F) between two charges
- Formula: F = k(Q1*Q2)/R²
- Constant k depends on the medium
Permittivity (ε): Affects the electric force between charges
- Formula with permittivity: F = (1/4πε) * (Q1*Q2)/R²
- Permittivity (ε) is specific to the medium
- Higher permittivity, lower force between charges
Physical Meaning: Permittivity allows its own field to decrease interaction between charges
- Medium property that affects the field between the charges
- Permittivity of a medium allows its field to weaken the interaction field between charges
Important concept: Greater the permittivity of the medium, lesser the force between charges*

Epsilon in Vacuum (ε0): Minimum
- Formula: ε0 = 8.85 x 10⁻¹² C²/N·m²
- Force is maximum in vacuum/free space
- Any medium's permittivity is greater than ε0
Examples of permittivity values in different media:
- Vacuum/Air: ε0 = 8.85 x 10⁻¹² C²/N·m²
- Water: ≈ 7.12 x 10⁻¹⁰ C²/N·m² (ε_water > ε_air)
- Glass: ≈ 3.01 x 10⁻¹¹ C²/N·m²

Simplification to avoid remembering multiple values
Definition: Permittivity of medium with respect to air
- Ratio: εr = ε_medium / ε_air
- Indicates how many times the permittivity of a medium is greater than that of air
Formula: ε_medium = εr * ε_air
Examples:
- Water εr = 81 ➔ ε_water = 81 * ε_air
- Glass εr = 7 ➔ ε_glass = 7 * ε_air
Force Relation: Force in medium is related to force in air:
- F_medium = F_air / εr*

Example 1: Air to Medium Force Calculation
- Given: F in air, F in medium
- Find εr (Relative Permittivity)
Example 2: Conceptual Change with Distance
- Charges Q1, Q2, separation D
- Force in air F becomes F/2 in a medium
- Separation halved
- Calculate relative permittivity
Example Problem: JEE-Mains level
- Two spherical charged metallic spheres in vacuum and in a liquid
- Calculate dielectric constant (relative permittivity) of liquid

Permittivity affects the force between charges in different media
Permittivity of vacuum is minimum, greatest force in vacuum
Relative permittivity simplifies the understanding of permittivity in different media
Use of relative permittivity in problem-solving to determine forces and properties of media