Question

find the relationship between permittivity of free space, permeability of free space and speed of light in vacuum ​

Answer 1

Expressions for the electric and magnetic fields in free space contain the electric permittivity ε0 and magnetic permeability μ0 of free space. These two quantities are not independent but are related to "c", the speed of light and other electromagnetic waves. The magnetic constant μ0 = 4π x 10-7 T m/A is called the permeability of space. The permeabilities of most materials are very close to μ0 since most materials will be classified as either paramagnetic or diamagnetic. But in ferromagnetic materials the permeability may be very large and it is convenient to characterize the materials by a relative permeability.

This contains the force unit N for Newton and the unit A is the Ampere, the unit of electric current.

With the magnetic permeability established, the electric permittivity takes the value given by the relationship

c = 1/sqrt(ε0μ0)

where the speed of light is given by

c=2.99792458 x 10^8 m/s (exact)

This gives a value of free space permittivity

ε0 = 8.854187817 x 10^-12 F/m

which in practice is often used in the form

k = 1/4piε0 = 8.987552 X10^9 Nm^2/C^2 = Coulomb's constant

These expressions contain the units F for Farad, the unit of capacitance, and C for Coulomb, the unit of electric charge.

The electric permittivity is connected to the energy stored in an electric field. It is involved in the expression for capacitance because it affects the amount of charge which must be placed on a capacitor to achieve a certain net electric field. In the presence of a polarizable medium, it takes more charge to achieve a given net electric field and the effect of the medium is often stated in terms of a relative permittivity.

The magnetic permeability is connected to the energy stored in a magnetic field. It is involved in the expression for inductance because in the presence of a magnetizable medium, a larger amount of energy will be stored in the magnetic field for a given current through the coil. The effect of the medium is often stated in terms of a relative permeability.

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