Electromagnetic Wave Propagation MCQ Quiz in मल्याळम - Objective Question with Answer for Electromagnetic Wave Propagation - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Concept:

The voltage standing wave ratio is defined as the ratio of the maximum voltage (or current) to the minimum voltage (or current).

\(VSWR = \frac{{{{\rm{V}}_{{\rm{max}}}}}}{{{{\rm{V}}_{{\rm{min}}}}}} = \frac{{{{\rm{I}}_{{\rm{max}}.}}}}{{{{\rm{I}}_{{\rm{min}}.}}}}\;\)

This can also be written as:

\(VSWR = \frac{{1 + {\rm{|Γ| }}}}{{1 - {\rm{|Γ|}}}}\;\)

Γ = Reflection coefficient, defined as:

\({\rm{Γ }} = \frac{{{Z_L} - {Z_0}}}{{{Z_L} + {Z_0}}}\;\)

ZL = Load impedance

Z0 = Characteristic Impedance

Calculation:

Given:

Z0 = Z₀ Ω

Z_L = -jZ0 Ω

\({\rm{Γ }} = \frac{{{Z_L} - {Z_0}}}{{{Z_L} + {Z_0}}}\;\)

\({\rm{Γ }} = \frac{{-jZ_0 - Z_0}}{{-jZ_0 + Z_0}} = \frac{-1-j}{1-j}=\frac{\sqrt2\angle -135^{\circ}}{\sqrt 2\angle-45^{\circ}}=1\angle -90^\circ\)

Γ = -j

Now:

\(VSWR = \frac{{1 + |-j|}}{{1 - |-j|}} =\frac{1+1}{1-1}=\frac{2}{0}= \infty\)

Poynting vector:

It states that the cross product of electric field vector (E) and magnetic field vector (H) at any point is a measure of the rate of flow of electromagnetic energy per unit area at that point that is 

\( \vec S = \vec E \times \vec H\)

Where P = Poynting vector,

E = Electric field and

H = Magnetic field

Or, it can be written as,

\(S = \frac{Power}{Area}\)

The Poynting vector describes the magnitude and direction of the flow of energy in electromagnetic waves.

The unit of the Poynting vector is watt/m2.

Additional Information

1) The Poynting vector (i.e. energy flow per unit area per unit time) for a plane electromagnetic wave is given by

\( \vec S = \frac{1}{\mu_o}(\vec E \times \vec H)\)

\( S = \frac{1}{\mu_o}(E H\, sin\theta )\)

2) From the above, it is clear that E and H are mutually perpendicular and also they are perpendicular to the direction of propagation of the wave.

Thus, the direction of the Poynting vector is along the direction of the propagation of the electromagnetic wave.

The Poynting vector describes the magnitude and direction of the flow of energy in electromagnetic waves per unit volume.

∴ The dimensions of both the Poynting vector and the electromagnetic power density are the same, i.e. M1 L-1 T-2

where M = Mass, L = Length, T = Time

Concept:

Loss tangent is given by, \(\tan \delta = \frac{\sigma }{{\omega \varepsilon }}\)

Where ω is the frequency is rad/sec

Loss tangents represent the dissipation of electromagnetic energy of dielectric material.

Calculation:

The given material is nonmagnetic lossy dielectric medium i.e. σ ≠ 0.

Real permittivity, ε_r = 2.25

Conductivity, σ = 10^-4 mho/m

For nonmagnetic material, μ_r = 1

Frequency of EM wave = 2.5 × 10⁶ Hz

\(\tan \delta = \frac{{{{10}^{ - 4}}}}{{2\pi\; \times \;2.5\; \times \;{{10}^6}\; \times \;\frac{1}{{36\pi }}\; \times \;{{10}^{ - 9}}\; \times \;2.25}} = 0.32\)  

Relative permeability (μ_r) = 200

Conductivity (σ) = 5 × 10⁶ mho/m

Outer diameter of conductor = 8 mm

Length of conductor = 2 mm

Total current carried by conductor, i(t) = 2 cos (π × 10⁴t) Amp

⇒ ω = π × 10⁴ rad/sec

⇒ f = 0.5 × 10⁴ Hz

\(\delta = \frac{1}{{\sqrt {\pi f\;\sigma \;{\mu _0}{\mu _r}} }}\)

\(\delta = \frac{1}{{\sqrt {\pi\; \times \;0.5\; \times \;{{10}^4}\; \times \;4\pi\; \times \;{{10}^{ - 7}}\; \times \;200\; \times \;5 \;\times\; {{10}^6}} }}\)

\(\Rightarrow \delta = \frac{1}{{\sqrt {2{\pi ^2}\; \times \;{{10}^6}} }} = 0.225\;mm\)

Analysis:

A conductor placed in a static field will exhibit or induce a charge on its surface so as to have zero fields inside it. i.e. for an ideal conductor, the electric & magnetic field inside it is zero.

The given situation can be visualized as shown:

A conductor dielectric interface satisfies the following boundary conditions:

H_1t – H_2t = J_s

B_1n = B_2n

E_1t = E_2t = 0

D_1n – D_2n = ρ_s

For a conductor: H_2t = E_2t = B_2n = D_2n = 0

So, H_1t = J_s

B_1n = B_2n = 0

E_1t = E_2t = 0

D_1n = ρ_s

• Under the electromagnetic spectrum, visible light has the lowest frequency among the given option.
• The spectrum ranges from radio waves having low frequency till gamma rays, having the highest one.

Permittivity: The property of any material which opposes the formation of an electric field is called permittivity.

The permittivity of free space is denoted by ϵ0.

Permeability: The measurement of the ability of any material that allows the formation of magnetic lines of force is called permeability.

The permeability of free space is given by μ0.

Notes:

• The larger the tendency for charge distortion (also called electric polarization), the larger the value of the permittivity
• This constant is equal to approximately 8.85 × 10-12 farad per meter (F/m) in free space (a vacuum)
• In other materials, it can be much different, often substantially greater than the free-space value

The characteristic impedance of a wave traveling in a lossy medium is given by:

\(Z = \sqrt {\frac{{j\omega μ }}{{\sigma + j\omega ϵ}}}\)

Put σ = 0 (free space and lossless medium)

\(Z = \sqrt {\frac{μ_0 }{ϵ_0}}\)

Where,

μ₀ = Permeability of free space = 4π x 10^-7 H / m

ϵ₀ = Permittivity of free space = 8.85 x 10^-12 F/m

CONCEPT:

• The skin effect is the tendency of an alternating electric current to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases with greater depths in the conductor.
• The electric current flows mainly at the skin of the conductor, between the outer surface and a level called the skin depth.
• Skin depth is defined as the reciprocal of attenuation constant i.e.,

\(\delta=\frac{1}{\alpha}\)

• The attenuation constant is given by:

\(\Rightarrow\alpha=\omega\sqrt{\frac{\mu\epsilon}{2}\left[\sqrt{1+\left(\frac{σ}{\omega\epsilon}\right)^2}-1\right]}\)

• For an ideal conductor with σ ≈ ∞,

\(\Rightarrow \delta=\frac{1}{\alpha}=\left[\sqrt{1+\left(\frac{σ}{\omega\epsilon}\right)^2}-1\right]≈\frac{σ}{\omega\epsilon}\)

CALCULATION:

Given α = 400 /m

Skin depth is defined as the reciprocal of attenuation constant i.e.,

\(\Rightarrow \delta=\frac{1}{\alpha}\)

\(\Rightarrow \delta=\frac{1}{400}=2.5~mm\)

α is the attenuation constant given by:

\(α=\omega\sqrt{\frac{\mu\epsilon}{2}\left[\sqrt{1+\left(\frac{σ}{\omega\epsilon}\right)^2}-1\right]}\)

ω = Operating frequency

μ = Permeability of the material

σ = Conductivity of the material

For a good conductor σ >> 1. The above expression for the attenuation constant can be approximated as:

\(α=\left[\sqrt{1+\left(\frac{σ}{\omega\epsilon}\right)^2}-1\right]≈\frac{σ}{\omega\epsilon}\)

∴ The attenuation constant becomes:

\(α=\omega \sqrt{\left(\frac{\muσ}{2\omega}\right)}\)

\(α=\sqrt{\left(\frac{\omega\muσ} {2}\right)}\)

\(\therefore~α =\sqrt{\pi f\muσ}\)

Thus, the skin depth becomes:

\(\delta=\frac{1}{\sqrt{\pi f \muσ}}\)

Note: The skin depth is inversely proportional to the square root of frequency.

Calculation:

According to Brewster's law, reflected rays are completely polarized and refracted rays are partially polarized.