.An industrial carbon dioxide laser produces a beam of radiation with average power of \(6.00 \mathrm{~kW}\) at a wavelength of \(10.6 \mu \mathrm{m}\). Such a laser can be used to cut steel up to \(25 \mathrm{~mm}\) thick. The laser light is polarized in the \(x\) -direction, travels in the positive \(z\) -direction, and is collimated (neither diverging or converging) at a constant diameter of \(100.0 \mu \mathrm{m} .\) Write the equations for the laser light's electric and magnetic fields as a function of time and of position \(z\) along the beam. Recall that \(\vec{E}\) and \(\vec{B}\) are vectors. Leave the overall phase unspecified, but be sure to check the relative phase between \(\vec{E}\) and \(\vec{B}\) .

Question: Determine the equations for the electric and magnetic fields of an industrial carbon dioxide laser beam as a function of time and position \(z\) along the beam, given the laser's average power is \(6.00 \mathrm{~kW}\), the beam diameter is \(100.0 \mu \mathrm{m}\), and the wavelength of the light produced by the laser is \(10.6 \mu \mathrm{m}\). The electric field is polarized in the \(x\)-direction, and the magnetic field is polarized in the \(y\)-direction. Answer: The equations for the electric and magnetic fields of the industrial carbon dioxide laser as a function of time and position along the beam are: \(\vec{E}(z, t) = E_0 \cos{(kz - \omega t)} \hat{x}\) \(\vec{B}(z, t) = B_0 \cos{(kz - \omega t)} \hat{y}\) where \(E_0\) represents the electric field amplitude, \(B_0\) represents the magnetic field amplitude, \(k\) is the wave number, \(\omega\) is the angular frequency, and \(\hat{x}\) and \(\hat{y}\) are unit vectors in the \(x\) and \(y\) directions, respectively.