An industrial laser is used to burn a hole through a piece of metal. The average intensity of the light is = 4.84 × 109 W/m2. What is the rms value of (a) the electric field and (b) the magnetic field in the electromagnetic wave emitted by the laser?
To find the rms value of the electric field and the magnetic field in the electromagnetic wave emitted by the laser, we can use the following equations:
(a) For the rms value of the electric field (E_rms):
E_rms = √(2 × ε₀ × c × I_avg)
Where:
E_rms is the rms value of the electric field
ε₀ is the vacuum permittivity (8.854 × 10^-12 C^2/N∙m^2)
c is the speed of light in a vacuum (3.00 × 10^8 m/s)
I_avg is the average intensity of the light
(b) For the rms value of the magnetic field (B_rms):
B_rms = √(μ₀ × I_avg)
Where:
B_rms is the rms value of the magnetic field
μ₀ is the vacuum permeability (4π × 10^-7 T∙m/A)
I_avg is the average intensity of the light
Now, let's calculate the values:
(a) Electric field (E_rms):
E_rms = √(2 × ε₀ × c × I_avg)
E_rms = √(2 × 8.854 × 10^-12 C^2/N∙m^2 × 3.00 × 10^8 m/s × 4.84 × 10^9 W/m^2)
Calculating this, we find:
E_rms ≈ 2.37 × 10^5 V/m
So, the rms value of the electric field emitted by the laser is approximately 2.37 × 10^5 V/m.
(b) Magnetic field (B_rms):
B_rms = √(μ₀ × I_avg)
B_rms = √(4π × 10^-7 T∙m/A × 4.84 × 10^9 W/m^2)
Calculating this, we find:
B_rms ≈ 3.82 × 10^-3 T
So, the rms value of the magnetic field emitted by the laser is approximately 3.82 × 10^-3 T.
Therefore, the rms values of the electric field and the magnetic field in the electromagnetic wave emitted by the laser are approximately 2.37 × 10^5 V/m and 3.82 × 10^-3 T, respectively.