Question

A 12.8-mW laser puts out a narrow beam 2.50 mm in diameter. Suppose that the beam is in free space.

1) What is the rms value of E in the beam? Erms= ?

2) What is the rms value of B in the beam? Brms=?

Answer 1

Given

power of the laser is P = 12.8 mW

diameter of the laser beam is d = 2.50 mm , radius r = 1.25 mm

the beam is in free space  

1)

from the relation P/A = c*epsilon0*E_rms^2

E_rms^2 = P/c*epsilon0*A

E_rms = sqrt(P/c*epsilon0*A )

C is speed of light , epsilon0 is permitivity of free space , A is area

E_rms = sqrt(P/c*epsilon0*pi*r^2)

substituting the values

E_rms = sqrt((12.8*10^-3)/(3*10^8*8.854*10^-12*pi*(1.25*10^-3)^2) V/m

E_rms = 990.808 V/m

2)

and from the relation

c = Erms/Brms

Brms = Erms/c

Brms = 990.808 /(3*10^8) T

Brms = 3.3027*10^-6 T