# Intensity of Electromagnetic Waves

• diethaltao
In summary: Well, I already knew Bx and By, I just didn't know how to find Bo. Thanks though!In summary, the intensity of a plane monochromatic electromagnetic wave with a wavelength of 2.2 cm and magnetic field described by \vec{B} = (Bx\vec{i} + By\vec{j})cos(kz+ωt) where Bx = 1.8E-6 T and By = 3.8E-6 T can be found by first determining the electric field amplitude E_0 using the equation E_0 = cB_0, where B_0 is the amplitude of the magnetic field wave found using the pythagorean theorem. This can then be plugged
diethaltao

## Homework Statement

A plane monochromatic electromagnetic wave with wavelength λ = 2.2 cm, propagates through a vacuum. Its magnetic field is described by
$\vec{B}$ = (Bx$\vec{i}$ + By$\vec{j}$)cos(kz+ωt)
where Bx = 1.8E-6 T and By = 3.8E-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively.

What is I, the intensity of this wave?

## Homework Equations

I = P/A = (1/2)cεoE^2
k = (2π)/λ
ω = ck
Bo*c = Eo

## The Attempt at a Solution

I found frequency to be c/λ = 13.63GHz.

I have tried setting t to zero in the given equation and plugging in k and ω to find B, then multiplying that by the speed of light to find E.
I then plugged that into I = (1/2)cεoE^2, but that gave me the wrong answer.

I've also tried adding to the two vectors and assumed that equaled Bo (which I don't think it does), and used Bo = (√2ZoI)/c where Zo = 377 ohms.
I've tried <B^2> = (Bo^2)/2 as well.

Is there an important equation I'm missing?

You need to understand what the symbols in the various formulas you have represent. In the expression for the intensity ##I##, ##E## is the amplitude of the electric field wave, what you later called ##E_0##. You can find ##B_0## from the expression for ##\vec B## and then use ##E_0 = cB_0## to find the electric field amplitude to plug into the intensity formula.

Delta2
In addition to what @vela said, you might find also rather obvious to use pythagorean theorem to find ##B_0## , $$B_0=\sqrt{B_x^2+B_y^2}$$

## 1. What is intensity of electromagnetic waves?

The intensity of electromagnetic waves refers to the strength or power of the wave. It is a measure of the amount of energy passing through a given area per unit time. Intensity is typically measured in watts per square meter (W/m2).

## 2. How is the intensity of electromagnetic waves related to their frequency and amplitude?

The intensity of electromagnetic waves is directly proportional to their frequency and the square of their amplitude. This means that as the frequency or amplitude increases, the intensity also increases.

## 3. What factors affect the intensity of electromagnetic waves?

The intensity of electromagnetic waves can be affected by various factors, such as the distance from the source, the medium through which the waves are traveling, and any obstacles or barriers that may be present in their path. Additionally, the intensity can also be affected by the properties of the source itself, such as its power and directionality.

## 4. How is the intensity of electromagnetic waves measured?

The intensity of electromagnetic waves can be measured using instruments such as power meters or radiometers. These devices measure the power of the waves over a specific area and can provide a numerical value for the intensity in watts per square meter.

## 5. Can the intensity of electromagnetic waves be harmful?

At certain levels, the intensity of electromagnetic waves can be harmful to living organisms. For example, exposure to high levels of UV radiation can cause skin damage and increase the risk of skin cancer. However, most electromagnetic waves at low intensities are not harmful and are essential for various technologies and communication systems.

Replies
8
Views
418
Replies
2
Views
6K
Replies
3
Views
2K
Replies
2
Views
253
Replies
2
Views
649
Replies
6
Views
1K
Replies
6
Views
2K
Replies
12
Views
839
Replies
3
Views
2K
Replies
2
Views
1K