An industrial laser is used to burn a hole through a piece of metal. The average density of the light is S = 1.22 109 W/m2. What is the rms value of each of the following fields in the electromagnetic wave emitted by the laser?
(a) the electric field
_________N/C
(b) the magnetic field
_________T
energy wise, 1/2 the power is carried in each field. Use that to find E and B.
Thanks!
To find the rms value of the electric field and magnetic field in the electromagnetic wave emitted by the laser, we can use the relationship between the power density (S) and the electric field (E) and magnetic field (B) of an electromagnetic wave.
The relationship is given by:
S = (1/2) * ε₀ * c * E₀²
where ε₀ is the vacuum permittivity (8.854 x 10⁻¹² F/m), c is the speed of light in vacuum (3 x 10⁸ m/s), and E₀ is the amplitude of the electric field.
Let's calculate the rms value for each field:
(a) Electric Field (E):
From the given power density S = 1.22 x 10⁹ W/m², we need to calculate the amplitude of the electric field (E₀).
Rearranging the equation above, we get:
E₀ = √(2S / ε₀c)
Substituting the given values, we have:
E₀ = √((2 * 1.22 x 10⁹ W/m²) / (8.854 x 10⁻¹² F/m * 3 x 10⁸ m/s))
Now, we can calculate E, the rms value of the electric field by dividing E₀ by √2:
E = E₀ / √2
(b) Magnetic Field (B):
The magnetic field (B) is related to the electric field (E) by the equation:
B = E / c
Now, let's calculate the values for electric field (E) and magnetic field (B):
(a) Electric Field (E):
Calculate E₀:
E₀ = √((2 * 1.22 x 10⁹ W/m²) / (8.854 x 10⁻¹² F/m * 3 x 10⁸ m/s))
Then calculate E:
E = E₀ / √2
(b) Magnetic Field (B):
Calculate B:
B = E / c
By following these steps and substituting the values, you can find the values for the electric field (E) in N/C and the magnetic field (B) in T emitted by the laser.