An industrial laser is used to burn a hole through a piece of metal. The average intensity of the light is S = 1.13 109 W/m2. What is the rms value of each of the following fields in the electromagnetic wave emitted by the laser?
(a) electric field
(b) magnetic field
You can solve for Emax by this
S=(1/munaught*2*speedlight)Em^2
Then solve for Bmax from Em/Bm= speedlight
then the rms value of each is 1/sqrt2 * max value
thanks!
To find the rms value of the electric field and magnetic field of the electromagnetic wave emitted by the laser, we can use the formula:
E = c * sqrt(S)
B = sqrt(S / (c * μ0))
Where:
E = rms value of the electric field
B = rms value of the magnetic field
c = speed of light in a vacuum (approximately 3.0 * 10^8 m/s)
μ0 = permeability of free space (approximately 4π * 10^-7 T m/A)
S = average intensity of the light in W/m^2
Let's calculate them step-by-step:
(a) Electric Field (E):
E = c * sqrt(S)
E = (3.0 * 10^8 m/s) * sqrt(1.13 * 10^9 W/m^2)
Calculating the square root:
E ≈ 3.0 * 10^8 m/s * (1.06 * 10^5 W/m)
E ≈ 3.18 * 10^13 V/m
Therefore, the rms value of the electric field is approximately 3.18 * 10^13 V/m.
(b) Magnetic Field (B):
B = sqrt(S / (c * μ0))
B = sqrt((1.13 * 10^9 W/m^2) / ((3.0 * 10^8 m/s) * (4π * 10^-7 T m/A)))
Simplifying:
B = sqrt((1.13 * 10^9 W/m^2) / (3.0 * 10^8 m/s * 4π * 10^-7 T m/A))
B = sqrt(3.773 * 10^1 T)
Calculating the square root:
B ≈ 6.14 T
Therefore, the rms value of the magnetic field is approximately 6.14 T.
To find the RMS value of the electric and magnetic fields, we first need to know the average intensity of the light. The intensity of an electromagnetic wave is related to the electric and magnetic fields by the equation:
I = cε0E^2
Where I is the intensity, c is the speed of light, ε0 is the permittivity of free space, and E is the electric field.
From the given information, we know that the average intensity (I) is 1.13x10^9 W/m^2. We can rearrange the equation to solve for the electric field (E):
E = sqrt(I / (cε0))
Now we need to find the value of c (speed of light) and ε0 (permittivity of free space):
c = 3x10^8 m/s
ε0 = 8.85x10^-12 F/m
Substituting these values into the equation, we get:
E = sqrt(1.13x10^9 / (3x10^8 x 8.85x10^-12))
Calculating this, we find the value of the electric field (E) to be approximately 3.77x10^4 V/m.
For the magnetic field, we can use the relationship between the electric field (E) and magnetic field (B):
B = E / c
Substituting the values we have:
B = (3.77x10^4) / (3x10^8)
Calculating this, we find the value of the magnetic field (B) to be approximately 1.26x10^-4 T.
Therefore, the RMS value of the electric field is approximately 3.77x10^4 V/m, and the RMS value of the magnetic field is approximately 1.26x10^-4 T.