Electromagnetism - Phase Velocities

Phase Velocities

Force F = power/c (in absorbing bodies) F= 2power/c 

(In case of mirror or perfectly reflecting bodies).

Intensity i = 1/2ε0 E20c.

Energy density (energy / volume) = 1 / 2 ε₀E₀² = B²₀ / 2μ₀

Λ = c/f f --> frequency, λ --> wavelength.

ω/k = c = E₀/B₀ 

Guide wavelength 

Λg = Vphase / f = vphase / c/ λ = Vphase λ/C

Group and phases velocities

V phase = c / 1 - (λ / 2a)²

Where a is width of the guide and λ is free space wavelength.

V group = c [1 - (λ/2a)²]

In free space or vacuum a --> ∞, therefore Vphase = Vgroup =  c

Pointing vector p = 1/ μ₀ E x B describes rate of energy flow per unit area in a place electromagnetic wave unit of p is Wm^-2

P = E₀ B₀ / 2μ₀ power per unit area.

If h is the height of antenna then program can be received upto a radius of 

R = 2hR where R is radius of earth 

Amplitude modulation (AM) if amplitude of carrier wave varies in accordance with instantaneous value of modulating signal then AM results

If ec = Ec sin ωct is scarier wave and em = Em sin ω mt is modulating signal

Then e = Ec (1 + ma sin ωmt) sin ωct is modulated signal where, ma = E_m / E_c = E _max - E _max / E _max+ E main is amplitude modulation index. 

Advantages of AM:-  it can be used for long distance communication.

Disadvantage it gives a very large noise.

Frequency range of interest:-  550 kHz to 30 MHz

Frequency modulation:-  if frequency of the carrier wave is varied in accordance with instantaneous value of modulating signal then FM results.

If e_c = E_c sin ωct is carrier wave

E_m = E_m sin ωmt is modulating signal.

Then e = E_c sin (ωC + k E m sin ωmt) t

Represents frequency modulated signal k is conversion factor which converts voltage to frequency.

Advantages of FM noise immune as amplitude does not vary and hence carries no information. Information is carried by frequency variation.

Disadvantages of FM
    
Short distance communication.
    
Costly equipment.

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