A 27 mW laser beam has a cross-sectional maximum electric field in this electromagnetic wave is given by :
[Given permittivity of space `in_(0) = 9 xx 10^(12)` SI units, Speed of light `c= 3 xx 10^(8) m//s`]

Options

A. `1kV//m`
B. `0.7 kV //m`
C. `2kV//m`
D. `1.4 kV //m`

Answer

D

Explanation

`I=1/2 n c in_0 E^2`
Where, n is refractive index, for air `n=1`.
` I=1/2 c .epsi_0 E^2 " " …..(i)`
Also`,I=(P)/(A ) " " …….(ii)`
From Eq. (i) and (ii), we get
`1/2 c epsi_0 E^2 = (P)/(A) "or" 1/2 c epsi_0 E^2 =(P )/(A ) or E=sqrt((2 xx 27 xx 10^(-3))/(10 xx 10^(-6) xx 3 xx 10 ^8 xx 9 xx 10^(-12)))`
`~= 1.4 xx 10^3 V//m =1.4 kV //m`