A laser emits 1.44*10^18 photons per second in a beam of light that has a diameter of 1.98 mm and a wavelength of 524.5 nm.
(a) Determine the average electric field strength
(b) Determine the average magnetic field strength for the electromagnetic wave that constitutes the beam.
You know the energy (given wavelenght and the number of photons)
http://en.wikipedia.org/wiki/Poynting_vector
You know the Poynting vector (watts/m^2) in the beam, so figure E and B.
check my thinking.
still don't understand where does wavelength and number of photons go too? do you divdide them to get energy or what?
You get energy per photon from Planck's equation, then multiply by the nubmer to get joules/second (watts).
To determine the average electric and magnetic field strengths for the given laser beam, we need to use the formulas related to electromagnetic waves.
The average electric field strength is given by the equation:
E = c * sqrt(2 * n * h * f / A)
Where:
E = electric field strength
c = speed of light in a vacuum (approximately 3 * 10^8 m/s)
n = number of photons emitted per second (1.44 * 10^18 photons per second)
h = Planck's constant (approximately 6.626 * 10^-34 J*s)
f = frequency of the wave (which can be calculated using the speed of light and the wavelength)
A = cross-sectional area the light beam (which can be calculated using the diameter)
Let's proceed with the calculations:
(a) Determining the average electric field strength:
Step 1: Calculate the frequency using the speed of light and the wavelength:
f = c / λ
Given: wavelength λ = 524.5 nm = 524.5 * 10^-9 m
Calculating: f = (3 * 10^8 m/s) / (524.5 * 10^-9 m) ≈ 5.72 * 10^14 Hz
Step 2: Calculate the cross-sectional area of the light beam using the diameter:
A = π * (d/2)^2
Given: diameter d = 1.98 mm = 1.98 * 10^-3 m
Calculating: A = π * ((1.98 * 10^-3 m) / 2)^2 ≈ 3.08 * 10^-6 m^2
Step 3: Calculate the average electric field strength using the given values:
E = (3 * 10^8 m/s) * sqrt(2 * (1.44 * 10^18) * (6.626 * 10^-34 J*s) * (5.72 * 10^14 Hz) / (3.08 * 10^-6 m^2))
Calculating: E ≈ 1.47 * 10^-7 V/m
Therefore, the average electric field strength of the laser beam is approximately 1.47 * 10^-7 V/m.
(b) Determining the average magnetic field strength:
The average magnetic field strength can be determined using the equation:
B = E / c
Given: electric field strength E ≈ 1.47 * 10^-7 V/m
Calculating: B = (1.47 * 10^-7 V/m) / (3 * 10^8 m/s) ≈ 4.9 * 10^-16 T
Therefore, the average magnetic field strength of the laser beam is approximately 4.9 * 10^-16 T.