A uniform plane electromagnetic wave propagates in a lossless dielectric medium.

Question

A uniform plane electromagnetic wave propagates in a lossless dielectric medium. The electric field in the wave has the instantaneous expression

E(z,t) = iy 3 sin(3pi.109t + 100piz %u2013 600), V/m.

i)             What is the frequency of the wave in Hz?

ii)           What is the wavelength of the wave in m?

iii)          What is the direction of propagation of the wave?

iv)          What is the phase velocity of the wave?

v)            What is the relative refractive index of the wave?

vi)          What is the polarization of the wave?

NOTE: (a) The relative refractive index nr of a medium represents the                         wave slowness factor, i.e., nr = c/vph.

(b) The polarization of an electromagnetic wave refers to the locus of the tip of the electric field vector which is traced as t changes. Typically, the polarization is linear, circular (right or left circular about the direction of propagation), or elliptical (right or left elliptical about the direction of propagation)

Explanation / Answer

i) frequency= 3pi*10^9/2pi =1.5*10^9hz

ii) wavelength = 3*10^8/1.5*10^9 =0.2m

iii) direction of propogation is in ' Y ' direction as it is given that E(z,t) = iy 3 sin(3pi.109t + 100piz %u2013 600), V/m.

iv) phase velocity = wave length / time period= wave length * frequency

= 0.2*1.5*10^9=3*10^8 m/sec

v) relative refractive index nr=c/phase velocity

= 3*10^8/3*10^8=1

vi)in a lossless dielectric medium electric suseptibility is 1

polarisation = 8.85*10^(-12)*1* E

= 8.85*10^(-12)*1*iy 3 sin(3pi.109t + 100piz %u2013 600), C/m

=26.55 sin(3pi.109t + 100piz %u2013 600) *10^(-12) C/m

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