Question

A 14.0-mW helium–neon laser emits a beam of circular cross section with a diameter of 2.90 mm.

(a) Find the maximum electric field in the beam. ________kN/C

(b) What total energy is contained in a 1.00-m length of the beam?________ pJ

(c) Find the momentum carried by a 1.00-m length of the beam. _________kg · m/s

Answer 1

(a)

Intensity of light beam is given by,

I = P/A = P/(pi*r^2) = Emax^2/(2*0*c)

here, P = Power = 14.0 mW = 14.0*10^-3 W

r = radius of beam = 2.90/2 mm = 1.45*10^-3 m

Emax = maximum electric field = ??

0 = 4*pi*10^-7

c = 3*10^8 m/s

So, Emax = sqrt(P*2*0*c/(pi*r^2)) = sqrt[(14.0*10^-3)*2*(4*pi*10^-7)*(3*10^8)/(pi*(1.45*10^-3)^2)]

Emax = 1264.2 N/C

Emax = 1.26 kN/C

(b.)

Energy contained in beam is given by,

U = P*l/c

here, l = length of beam = 1.00 m

So, U = (14*10^-3)*1/(3*10^8) = 4.67*10^-11 J

U = 46.7 pJ

(c.)

Momentum carried by beam is given by,

p = U/c = (46.7 pJ)/(3*10^8 m/s)

p = (46.7*10^-12)/(3*10^8) kg.m/s

p = 1.56*10^-19 kg.m/s