Question

A laser pulse has an energy of 21 J and a beam radius of 2 mm. The pulse duration is 15 ns and the energy density is uniformly distributed within the pulse.

(a) What is the spatial length of the pulse?
m

(b) What is the energy density within the pulse?
kJ/m³

(c) Find the rms values of the electric and magnetic fields in the pulse.
E₀ =  MV/m
B₀ =  T

Answer 1

U= 21 J and r = 2*10^-3 m , t = 15*10^-9 s ,

c = 3*10^8 m/s

so now  

a) spatial length of the pulse L = c*t = 3*10^8* 15*10^-9 = 4.5 m

b)

the energy density within the pulse is u = U/LA = 21 /( 4.5*pi*(2*10^-3)^2) =371361.534 J

or  371.361 kJ/m^3

c)the intensity of beam is I = u*c = 371361.534*3*10^8 = 1.1140846e14 W/m^2

Erms = sqrt(2u/epsilon) = sqrt(2*371361.534 /(8.85*10^-12))

=289.695548 M V/m

Brms = Erms/c =289695548/ ( 3*10^8)  

=0.965651827 T answer