Question

write down the expression for the velocity of electromagnetic wave in a medium and hence find out an expression for the refractive index of the medium

Answer 1

Answer:

Electromagnetic (EM) waves are changing electric and magnetic fields, transporting energy and momentum through space.  EM waves are solutions of Maxwell's equations, which are the fundamental equations of electrodynamics.  EM waves require no medium, they can travel through empty space.  Sinusoidal plane waves are one type of electromagnetic waves.  Not all EM waves are sinusoidal plane waves, but all electromagnetic waves can be viewed as a linear superposition of sinusoidal plane waves traveling in arbitrary directions.  A plane EM wave traveling in the x-direction is of the form

E(x,t) = Emaxcos(kx - ωt + φ),  B(x,t) = Bmaxcos(kx - ωt + φ).

E is the electric field vector, and B is the magnetic field vector of the EM wave.  For electromagnetic waves E and B are always perpendicular to each other and perpendicular to the direction of propagation.  The direction of propagation is the direction of E x B.

If, for a wave traveling in the x-direction E = Ej, then B = Bk and j x k = i.  Electromagnetic waves are transverse waves.

The wave number is k = 2π/λ, where λ is the wavelength of the wave.  The frequency f of the wave is f = ω/2π, ω is the angular frequency.  The speed of any periodic wave is the product of its wavelength and frequency.

Answer 2

Answer:

The expression for the velocity of an electromagnetic wave in a medium is given as $v=\frac{1}{\sqrt{ue}}$

Refractive index is given as $n=\frac{1}{\sqrt{(u_r)(e_r)}}$

Explanation:

The expression for the velocity of an electromagnetic wave in a medium is given as $v=\frac{1}{\sqrt{ue}}$

where u is the permeability of the medium and e is its permittivity.

Expression for the refractive index of the medium.

The refractive index of any medium is given as $n=\frac{c}{v}$

Where c is the speed in air and v is the speed in a given medium.

And the value of c will be given as

$c=\frac{1}{\sqrt{(u_o)(e_o)}}$

where $u_0$ and $e_o$ are permeability of air and is its permittivity respectively.

And the value of v will be given as

$v=\frac{1}{\sqrt{ue}}$

where u is the permeability of the medium and e is its permittivity.

Therefore Refractive index n will be

    $n=\frac{c}{v}$

$n=\frac{\sqrt{ue}}{\sqrt{(u_o)(e_o)}}$

$n=\frac{\sqrt{ue}}{\sqrt{(u.u_r)(e.e_r)}}$

where $u_r$ and $e_r$ are the relative permeability of medium with air and its permittivity respectively.

$n=\frac{1}{\sqrt{(u_r)(e_r)}}$

Hence this is the required expression.

Reference Links

https://brainly.in/textbook-solutions/q-electromagnetic-waves?source=quick-results

https://brainly.in/textbook-solutions/q-velocity-electromagnetic-waves?source=quick-results

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