Permittivity of Free Space

Definition

Permittivity of free space, denoted as $\epsilon_0$, is a fundamental physical constant that represents the capacity of free space, or a vacuum, to support an electric field. It is a measure of the amount of charge required to create a unit of electric flux in a vacuum.

5 Must Know Facts For Your Next Test

1. The value of the permittivity of free space is approximately $8.854 \times 10^{-12}$ farads per meter (F/m).
2. Permittivity of free space is a crucial parameter in Coulomb's law, which describes the force between two point charges in a vacuum.
3. Permittivity of free space is used to calculate the electric field strength and electric flux density in a vacuum or free space.
4. The permittivity of free space is a fundamental constant that appears in Maxwell's equations, which describe the relationships between electric and magnetic fields.
5. The permittivity of free space is a universal constant that does not depend on the properties of any particular material or medium.

Review Questions

• Explain how the permittivity of free space is used in Coulomb's law to determine the force between two point charges.
  • Coulomb's law states that the force between two point charges in a vacuum is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The permittivity of free space, $\epsilon_0$, is a crucial parameter in Coulomb's law, as it represents the ability of free space to support an electric field. Specifically, Coulomb's law can be written as $F = \frac{q_1 q_2}{4\pi\epsilon_0 r^2}$, where $F$ is the force, $q_1$ and $q_2$ are the charges, and $r$ is the distance between them. The permittivity of free space, $\epsilon_0$, determines the strength of the electric field and, consequently, the force between the charges in a vacuum.
• Describe the role of the permittivity of free space in the calculation of electric flux density in a vacuum.
  • The permittivity of free space, $\epsilon_0$, is a fundamental constant that relates the electric field strength to the electric flux density in a vacuum. Specifically, the electric flux density, $\vec{D}$, is defined as $\vec{D} = \epsilon_0 \vec{E}$, where $\vec{E}$ is the electric field strength. This relationship shows that the permittivity of free space determines the amount of electric flux density that can be supported per unit of electric field strength in a vacuum. In other words, $\epsilon_0$ represents the capacity of free space to store electric energy, which is a crucial parameter in the study of electric fields and their interactions.
• Analyze the significance of the permittivity of free space in the context of Maxwell's equations and the behavior of electromagnetic waves in a vacuum.
  • The permittivity of free space, $\epsilon_0$, is a fundamental constant that appears in Maxwell's equations, which describe the relationships between electric and magnetic fields. Specifically, Maxwell's equations govern the propagation of electromagnetic waves, including light, in a vacuum. The permittivity of free space, along with the permeability of free space, $\mu_0$, determines the speed of electromagnetic waves in a vacuum, which is the speed of light, $c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$. Furthermore, the permittivity of free space is a crucial parameter in the wave equation, which describes the behavior of electromagnetic waves. The permittivity of free space, therefore, is essential in understanding the fundamental properties of electromagnetic radiation and its propagation through a vacuum, which is the basis for many applications in physics and engineering.

Related terms

Electric Flux Density: Electric flux density, or electric displacement, is a vector field that describes the electric flux per unit area of a surface perpendicular to the direction of the field.

Electric Constant: The electric constant, also known as the permittivity of free space, is a physical constant that describes the ability of free space to support an electric field.

Coulomb's Law: Coulomb's law is a fundamental principle in electrostatics that describes the force between two stationary, electrically charged particles.