The speed of light in vacuum is defined to be c=299792458 m / s=1 / √(μ0 ϵ0) . The permeability

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The speed of light in vacuum is defined to be c=299792458 m...

The speed of light in vacuum is defined to be $c=299792458 \mathrm{m} / \mathrm{s}=1 / \sqrt{\mu_{0} \epsilon_{0}}$ . The permeability constant of vacuum is defined to be $\mu_{0}=4 \pi \times 10^{-7} \mathrm{N} \cdot \mathrm{s}^{2} / \mathrm{C}^{2}$ . Use these definitions to calculate the value of $\epsilon_{0},$ the permittivity of free space, to eight significant figures.

Key Concepts

Speed of Light

The speed of light is a fundamental constant in physics that represents the maximum speed at which all energy, matter, and information in the universe can travel. It also plays a crucial role in both electromagnetic theory and the theory of relativity, serving as a linking constant between electric and magnetic fields in Maxwell's equations.

Vacuum Permeability

Vacuum permeability, commonly denoted as ??, is a constant that quantifies the ability of free space to support magnetic field formation. It is essential in the formulation of electromagnetic laws, such as Ampère's law, and appears in the derived relationships for wave propagation in a vacuum.

Vacuum Permittivity

Vacuum permittivity, denoted as ??, measures the resistance encountered when forming an electric field in a vacuum. It is a fundamental parameter in Coulomb's law and Maxwell's equations, playing a key role in the relationship between electric fields, charges, and the propagation of electromagnetic waves.

Electromagnetic Constants Relationship

The interrelationship between the speed of light, vacuum permeability, and vacuum permittivity is a cornerstone of electromagnetic theory, expressed by the equation c = 1/?(????). This equation not only defines the speed of light in vacuum in terms of these two constants but also illustrates the intrinsic link between electric and magnetic fields in a vacuum.

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