33.8:
Electromagnetic Waves in Matter
Unlike mechanical waves, electromagnetic waves can travel in a vacuum or in any material medium.
Consider the electromagnetic wave passing through a dielectric medium. In such a case, Maxwell's equations get modified.
In Ampere's law, ε0 is replaced with ε, the permittivity of the dielectric. Also, the vacuum permeability is replaced by the permeability of the medium.
Recall the relationships between the electric and magnetic fields derived using Faraday's and Ampere's law. Since the speed of the wave in a dielectric is not the same as in a vacuum, the constant "c" is replaced with a reduced velocity "v".
By comparing these two relations, the speed of an electromagnetic wave in a dielectric can be obtained.
Except for ferromagnetic materials, the relative permeability of most dielectrics is usually close to unity, and the dielectric constant is always greater than unity. Hence, the wave speed is always less compared to the speed in a vacuum.
The ratio of the speed of an electromagnetic wave in a vacuum to the speed in a material is known as the refractive index of the material.
33.8:
Electromagnetic Waves in Matter
Electromagnetic waves can travel in the vacuum as well as in matter. For example light, which is an electromagnetic wave, can travel through air, water, or glass.
Consider the electromagnetic wave passing through a dielectric medium. In such a case, Maxwell's equations get modified. In Ampere's law, ε0 , the dielectric permittivity of free space is replaced with ε, the permittivity of dielectric. Also, the vacuum permeability μ0 is replaced by the permeability of the medium, μ.
Furthermore, the constant speed, c is replaced with a reduced velocity, v in the expression for the relationships between electric and magnetic fields derived using Faraday's and Ampere's law. By comparing those two relations, the speed of an electromagnetic wave in a dielectric can be obtained.
For most dielectrics, the relative permeability κm is nearly equal to unity, excluding the insulating ferromagnetic materials. Since the dielectric constant κ is always greater than unity, the speed of electromagnetic waves in a dielectric is always less than the speed in the vacuum.
In Optics, the ratio of the speed in the vacuum to the speed in a material is known as the refractive index of the material. The dielectric constant is a function of frequency. For instance, dielectric constant for water is 80.4 for steady fields but it is approximately 1.8 in the frequency range of visible light.
Suggested Reading
- Young, H.D. and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson. Section 32.3; pages 1063–1064.