Question

A 400-W industrial carbon dioxide cutting laser is capable of cutting 3.0-mm thick steel at a rate of 20 mm/s. Carbon dioxide lasers operate at a wavelength of 10.6 μm. The spot size of the cutting laser is 0.16 mm in diameter and the intensity is uniform in this spot.

A.What is the magnitude of the Poynting vector for this laser?

Express your answer with the appropriate units.

B.What is the magnitude of the rms magnetic field for this laser?

Express your answer with the appropriate units.

C.What is the magnitude of the rms electric field for this laser?

Express your answer with the appropriate units.

Answer 1

Part A:

Poynting vector is given by energy crossing unit area normal to area.

S = Power/ Area normal to surface

Poynting vector, S = 400/[pi*(d/2)²]

given, diameter, d = 0.16mm = 0.16*10^-3 m

Poynting vector, S = 400/[pi*(0.16*10^-3/2)²] = 1.989*10¹⁰ W/m²

Poynting vector, S = 2.0*10¹⁰ W/m²

Part C:

The RMS value of the electric field is

E_rms = {1/sqrt[2]}*E_o

E_rms = sqrt[mu_o*c*S] = sqrt[4*pi*10-7*3*108*2.0*10¹⁰]

E_rms = 2.75*10⁶ V/m

Part B:

And the magnitude of the RMS magnetic field:

B_rms = E_rms /c = (2.75*10⁶) / (3*10⁸)

B_rms = 9.15*10^-3 T