Question

A small helium-neon laser emits red visible light with a power of 3.80 mW in a beam that has a diameter of 2.70 mm.

(a) What are the amplitudes of the electric and magnetic fields of the light?

Emax	=  V/m
Bmax	=  T

(b) What are the average energy densities associated with the electric field and with the magnetic field?

uE,av	=  J/m3
uB,av	=  J/m3

(c) What is the total energy contained in a 1.00-m length of the beam?
J

Answer 1

Given Data:

P = 3.80 mw = 3.80 x 10^-3 W

D = 2.70mm = 2.70 x 10^-3 m

Part A:

laser intensity I = P/A

I = 4P/D²

I = (4*3.80 x 10^-3)/[3.14*(2.70 x 10^-3)²]

I = 664.028 W/m²

and we also know that I = ½*_o*c*E²

E = sqrt(2I/oc)

E = sqrt(2*664.028/8.854 x 10^-12*3 x 10⁸)

E = sqrt(499983.43)

E_max = 707.1 V/m

and

B = E/c

B = (707.1)/(3 x 10⁸)

B_max = 2.357 x 10^-6 T

Part 2:

uB_av = uE_av = ¼*e_o­*E²_max

uB_av = ¼*8.854 x 10^-12­*707.1²

uB_av = 1.1 x 10^-6 J/m³

Part 3:

E_tot = u_tot*V

E_tot = 2*u_E*0.25**D²*L

E_tot = 2*1.1 x 10^-6*0.25*3.1415*0.0027²*1

E_tot = 1.2589 x 10^-11 J

E_tot = 1.26 x 10^-11 J