3.5 Electric Permittivity

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:

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

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!