Energy carried by Electromagnetic Waves

[Gannon]

Homework Statement

An industrial laser is used to burn a hole through a piece of metal. The average density of the light is S = 1.24E9 W/m2. What is the rms value of each of the following fields in the electromagnetic wave emitted by the laser?

Homework Equations

S = ce_oE²
S = (c/u_o)B²
E=cB
S is average density and E,B are rms values.

The Attempt at a Solution

Solving for E:
sqrt(S/ce_o) = E
sqrt(1.24E9/(3e8 x 8.85E-12)) = E = 683405.7 N/C

Solving for B:
E = cB
E/C = B
4.67E11/3E8 = .00228T

I have 5 tries to get this homework right and I'm down to my last one. I want to make sure I'm not leaving anything out this time. Any help is appreciated!

 

[Redbelly98]

Looks good. You might need to watch the significant figures on the answer for E, they checked for that.

 

[thomate1]

I would like to point out that the equations used in this attempt are not entirely accurate. The first equation, S = ceoE2, is only applicable for electromagnetic waves in vacuum. In this case, the laser is emitting the electromagnetic wave in a medium (metal), so the correct equation would be S = ceoE2/n, where n is the refractive index of the medium. Additionally, the second equation, S = (c/uo)B2, is only valid for magnetic fields in vacuum. In this situation, since the laser is emitting an electromagnetic wave in a medium, the correct equation would be S = (c/uo)B2/n, where n is the refractive index of the medium.

Furthermore, it is important to note that the average density of light (S) is not the same as the intensity of light. S represents the flow of energy per unit area, while intensity is the power per unit area. Therefore, the units for S are watts/meter^2, while the units for intensity are watts/meter^2/steradian.

To accurately solve this problem, we need to know the wavelength of the laser, as well as the refractive index of the metal. With this information, we can use the equations for power density and intensity to calculate the RMS values of the electric and magnetic fields.

In conclusion, as a scientist, I would suggest reviewing the correct equations and units for power density and intensity, as well as considering the medium in which the electromagnetic wave is propagating, in order to accurately solve this problem.