A 13.0-mW helium-neon laser emits a beam of circular cross section with a diameter of 3.10 mm.(a) Find the maximum electric field in the beam.(b) What total energy is contained in a 1.00-m length of the beam?(c) Find the momentum carried by a 1.00-m length of the beam.Step 1We will find the reasonable size of the electric field in a beam of bright light. At the speed of light, only a smallfraction of a joule is contained in a meter-length beam. The momentum of the beam is a very small fraction of akg. m/s. Light is described by energy and momentum but possesses no mass.Step 2We will use the equation relating the intensity of light to the wave amplitude. From the definition of intensity, wecan find the energy content of the beam of light. Then the relationship between momentum, energy, and thespeed of light will give us the momentum of a length of the beam.Step 3The intensity of light I is given by the average magnitude of the Poynting vector. We have2I = S₂avgPTr²Emax2μ0Cmaxwhere P is power, r is the radius of the beam, E, is the maximum value of the electric field, is the constantpermeability of free space, and c is the speed of light.

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A 13.0-mW helium-neon laser emits a beam of circular cross section with a diameter of 3.10 mm. (a) Find the maximum electric field in the beam. (b) What total energy is contained in a 1.00-m length of the beam? (c) Find the momentum carried by a 1.00-m length of the beam.

A 13.0-mW helium-neon laser emits a beam of circular cross section with a diameter of 3.10 mm. (a) Find the maximum electric field in the beam. (b) What total energy is contained in a 1.00-m length of the beam? (c) Find the momentum carried by a 1.00-m length of the beam.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A 13.0-mW helium-neon laser emits a beam of circular cross section with a diameter of 3.10 mm.
(a) Find the maximum electric field in the beam.
(b) What total energy is contained in a 1.00-m length of the beam?
(c) Find the momentum carried by a 1.00-m length of the beam.
Step 1
We will find the reasonable size of the electric field in a beam of bright light. At the speed of light, only a small
fraction of a joule is contained in a meter-length beam. The momentum of the beam is a very small fraction of a
kg. m/s. Light is described by energy and momentum but possesses no mass.
Step 2
We will use the equation relating the intensity of light to the wave amplitude. From the definition of intensity, we
can find the energy content of the beam of light. Then the relationship between momentum, energy, and the
speed of light will give us the momentum of a length of the beam.
Step 3
The intensity of light I is given by the average magnitude of the Poynting vector. We have
2
I = S₂
avg
P
Tr²
Emax
2μ0C
max
where P is power, r is the radius of the beam, E, is the maximum value of the electric field, is the constant
permeability of free space, and c is the speed of light.

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