Physics, 07.04.2020 16:54, kiingbr335yoqzaxs

He-Ne lasers are often used in physics demonstrations. They produce light of wavelength 633 nm and a power of 0.750 mW spread over a cylindrical beam 1.35 mm in diameter (although these quantities can vary).

Part A

What is the intensity of this laser beam?
I=W/m^2

Part B

What is the maximum value of the electric field?
Emax=V/m

Part C

What is the maximum value of the magnetic field?
Bmax=uT

Part D

What is the average energy density in the laser beam?
Uav=J/m^3

Answers: 3

Show answers

Answers

answered: bloodry

A) 524.0 W/m^2

B) 0.531 V/m

C) $1.77\cdot 10^{-3} \mu T$

D) $2.5\cdot 10^{-12} J/m^3$

Explanation:

The intensity of an electromagnetic wave is given by

$I=\frac{P}{A}$

where

I is the intensity

P is the power of the wave

A is the area over which the radiation is spread

In this problem:

$P=0.750 mW = 0.750\cdot 10^{-3}W$ is the power of the light emitted by the laser

This power spread over a cylindrical beam, so the area over which it spreads is the area of the base of the cylinder, which is the area of a circle:

$A=\pi (\frac{d}{2})^2$

where

$d=1.35 mm = 1.35\cdot 10^{-3} m$ is the diameter of the beam

Therefore, the intensity of the laser beam is:

$I=\frac{P}{\pi (\frac{d}{2})^2}=\frac{0.750\cdot 10^{-3}}{\pi (\frac{1.35\cdot 10^{-3}}{2})^2}=524.0 W/m^2$

The relationship between power of an electromagnetic wave and maximum value of the electric field is the following:

$P=\epsilon_0 E^2 c$

where

P is the power

$\epsilon_0$ is the vacuum permittivity

is the speed of light

E is the maximum value of the electric field

In this problem we have:

$P=0.750 mW = 0.750\cdot 10^{-3}W$ is the power of the light emitted by the laser

$\epsilon_0 =8.85\cdot 10^{-12} F/m$ is the vacuum permittivity

$c=3.0\cdot 10^8 m/s$ is the speed of light

Solving for E, we find the value of the electric field:

$E=\sqrt{\frac{P}{\epsilon_0 c}}=\sqrt{\frac{0.750\cdot 10^{-3}}{(8.85\cdot 10^{-12})(3.0\cdot 10^8)}}=0.531 V/m$

For an electromagnetic wave, the relationship between amplitude of the electric field and amplitude of the magnetic field is:

E=cB

where

E is the maximum value of the electric field

c is the speed of light

B is the maximum value of the magnetic field

In this problem we have:

E = 0.531 V/m is the maximum value of the electric field

$c=3.0\cdot 10^8 m/s$ is the speed of light

Solving the equation for B, we find the maximum value of the magnetic field:

$B=\frac{E}{c}=\frac{0.531}{3.0\cdot 10^8}=1.77\cdot 10^{-9} T = 1.77\cdot 10^{-3} \mu T$

The energy density of an electromagnetic wave is the amount of energy per unit volume of the wave.

The average energy density of an electromagnetic wave is related to the amplitude of the electric field by the equation:

$w=\epsilon_0 E^2$

where

w is the energy density

$\epsilon_0$ is the vacuum permittivity

E is the maximum value of the electric field

Here we have for this laser beam:

$\epsilon_0 =8.85\cdot 10^{-12} F/m$ is the vacuum permittivity

E = 0.531 V/m is the maximum value of the electric field

Substituting, we find the average energy density of the laser beam:

$w=(8.85\cdot 10^{-12})(0.531)^2=2.5\cdot 10^{-12} J/m^3$

answered: Guest

You will hear a hissing sound because of the carbon dioxide escaping the can or bottle

answered: Guest

answer///terminator or twilight zone;

Questions in other subjects:

History, 21.05.2020 05:02

Compare and contrast the strengths and weaknesses of the Union and the Confederacy following the outbreak of war in 1861. How well did each side take these factors into considerati...

History, 21.05.2020 05:02

Which of the following describes an effect of nationalism on European colonies during the 19th century?...

English, 21.05.2020 05:02

(1) Bob Dylan is the songwriter who opened up the doors of possibility to all who followed. (2) He was the mysterious bard with a guitar who sent out a clarion call—first as the ac...

Biology, 21.05.2020 05:02

Explain what a Food web and Food chain is Please help! I have an test tomorrow <3...

English, 21.05.2020 05:02

"How art thou out of breath, when thou hast breath to say to me that thou art out of breath? The excuse that thou dost make in this delay is longer than the tale thou d...

Social Studies, 21.05.2020 05:02

Which of the following are techniques that companies use to influence consumer demand for their goods and services '...

Engineering, 21.05.2020 05:02

G Consider a beam of material subject to an axial load, a strain gauge is laminated on the top of the beam and aligned along the axis of loading. The strain gauge is subject to an...

Biology, 21.05.2020 05:02

Use the drop-down menus to complete the sentence. The image shows a type of reproduction called ....

History, 21.05.2020 05:02

What influences the effectiveness of a site? During the area of New France, the site of the new colonies greatly favored the colonists. Why? (it was an advantage to the colonists,...

English, 21.05.2020 05:02

(1) Each state should enact a law that makes wearing seat belts mandatory for all passengers and drivers in cars and trucks. (2) Statistics show that seat belts reduce serious cras...

Other tasks in the category: Physics More task

Answers

Other questions on the subject: Physics

Questions in other subjects: