3.5 Electric Permittivity
Coulomb’s Law Constant
In this section, we’ll introduce some important constants used in electricity: Coulomb’s Constant () and Permittivity ().
What is Coulomb’s Constant?
Coulomb’s constant simplifies calculations in electromagnetism. It appears in Coulomb’s Law, which describes the electrical force between two charged particles:
: Electrical force.
, : Charges of particles.
: Distance between charges.
: Coulomb’s constant, approximately .
Historical Context
Oliver Heaviside noticed that many electromagnetism equations included . To simplify, he introduced as shorthand. Though not essential, it makes calculations more straightforward.
Permeability vs. Permittivity
Permeability and Permittivity describe how materials interact with electromagnetic waves:
| Property | Description | Symbol |
|---|---|---|
| Permittivity | Measures resistance to electric fields | |
| Permeability | Measures resistance to magnetic fields |
Connection to Electromagnetic Waves
Permittivity and permeability relate to the speed of light :
This connection highlights their importance in both electricity and magnetism.
Electric Permittivity
Permittivity quantifies how an electric field influences and is influenced by a medium.
Permittivity of Free Space
Represents a vacuum’s permittivity.
.
Relative Permittivity
Also known as the dielectric constant.
Calculated as:
Relative permittivity compares a material’s ability to transmit electric fields to that of a vacuum.
Example Permittivity Values
| Substance | Permittivity | Relative Permittivity |
| Vacuum | 1.00000 | |
| Air | 1.00054 | |
| Paper | 3 | |
| Water | 80 |
Note: The relative permittivity of air is so close to 1 that, for simplicity, we often treat air as a vacuum in calculations.
Practice Question
Question:
Body tissue has a relative permittivity of 8. What is its absolute permittivity?
Solution:
Given: , .
Absolute permittivity:
Answer:
The permittivity of body tissue is approximately .
Understanding permittivity is crucial for exploring electric fields, circuits, and electromagnetic waves. Mastery of this concept lays the groundwork for more advanced topics in physics!
