# Calculating Radius of Circular Area from Laser Power and Energy Density

• Dart82
In summary, for a laser beam with an energy density of 9.5x10^-8 J/m cubed and a power of 15W, the radius of the circular area it delivers power to is 0.41 meters. This can be calculated by first finding the intensity of the beam by multiplying the speed of light by the energy density, and then finding the area using the formula P/S.
Dart82

## Homework Statement

energy density in a laser beam is 9.5x10^-8 J/m cubed. the laser beam is cylindrical, and it delivers a power of 15W to a certain area. What is the radius of this circular area?

## Homework Equations

Intensity :
S=cu and S=Power/Area
Area of a circle (or possibly the area of a cylinder?)

## The Attempt at a Solution

first i find the intensity by multiplying the speed of light by the energy density in the laser: (2.994x10^8)x(9.5x10^-8)=28.44
Then i find the Area using S=P/A: 28.44/15W=1.89m
Using the area of a circle: 1.89=pi*radius^2. According to my calculations, my radius would be .78 meters. The correct answer is supposed to be 0.41 meters. Can someone please tell me where i am screwing this one up

Dart82 said:

## Homework Statement

energy density in a laser beam is 9.5x10^-8 J/m cubed. the laser beam is cylindrical, and it delivers a power of 15W to a certain area. What is the radius of this circular area?

## Homework Equations

Intensity :
S=cu and S=Power/Area
Area of a circle (or possibly the area of a cylinder?)

## The Attempt at a Solution

first i find the intensity by multiplying the speed of light by the energy density in the laser: (2.994x10^8)x(9.5x10^-8)=28.44
Then i find the Area using S=P/A: 28.44/15W=1.89m
Using the area of a circle: 1.89=pi*radius^2. According to my calculations, my radius would be .78 meters. The correct answer is supposed to be 0.41 meters. Can someone please tell me where i am screwing this one up

You made a math error. You accidently calculated S/P for the area, when it should be P/S. So it should be 15W/28.44 instead of what you have.

ohhhhh...that would seem to be a problem. thanks!

## 1. What is an EM wave?

An EM wave, or electromagnetic wave, is a type of energy that is produced when an electric field and a magnetic field oscillate and intersect with each other.

## 2. How does an EM wave carry energy?

EM waves carry energy through the oscillation of the electric and magnetic fields. As the fields oscillate, they create a disturbance in the particles of the medium they are traveling through, transferring energy to those particles.

## 3. What is the relationship between the energy of an EM wave and its frequency?

The energy of an EM wave is directly proportional to its frequency. This means that as the frequency of the wave increases, so does its energy.

## 4. Can an EM wave lose energy as it travels through space?

No, an EM wave does not lose energy as it travels through space, as it does not require a medium to propagate. However, it can transfer energy to particles in a medium it passes through.

## 5. How does the energy carried by an EM wave affect matter?

The energy carried by an EM wave can affect matter in various ways. For example, it can cause particles to vibrate, heat up, or even ionize. The specific effect depends on the type of matter and the intensity of the EM wave.

### Similar threads

• Introductory Physics Homework Help
Replies
4
Views
1K
• Electromagnetism
Replies
12
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
10K
• Engineering and Comp Sci Homework Help
Replies
34
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
5K
• Introductory Physics Homework Help
Replies
6
Views
5K
• Cosmology
Replies
9
Views
2K
• Advanced Physics Homework Help
Replies
1
Views
2K
• Advanced Physics Homework Help
Replies
8
Views
11K
• Advanced Physics Homework Help
Replies
3
Views
6K