ELECTROMAGNETIC WAVES

GROUP 3

OVERVIEW

This covers different areas related to electromagnetic waves. Electromagnetic waves, the cornerstone of modern physics, are characterized by oscillating electric and magnetic fields that traverse space without the need for a medium. The electromagnetic spectrum spans an array of frequencies, from the expansive reach of radio waves to the penetrating energy of gamma rays. These waves boast distinct properties, including wavelength, frequency, and speed, with their energy directly linked to frequency. Understanding electromagnetic phenomena is paramount across diverse disciplines, from telecommunications to astronomy, underscoring their pivotal role in shaping our understanding of the universe and advancing technology.

Electromagnetic Waves

Electromagnetic waves, first postulated by James Clerk Maxwell and subsequently confirmed by Heinrich Hertz, are the foundation of modern electromagnetism. They are also known as EM waves and are the composition of oscillating electric and magnetic fields. These waves emerge when an electric field interacts with a magnetic field, creating a self-propagating, transverse wave through space.

At their core, electromagnetic waves are solutions of Maxwell’s equations, which are the fundamental equations of electrodynamics. These equations elucidate how electric charges and currents generate electromagnetic fields, and how changes in these fields propagate as waves through space.

The Electromagnetic Spectrum

The electromagnetic spectrum encompasses all possible frequencies of electromagnetic radiation.
It ranges from low-frequency, long-wavelength radio waves to high-frequency, short- wavelength gamma rays.
Common segments of the spectrum include radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

Properties of Electromagnetic Waves

Wavelength (λ):The distance between successive peaks or troughs of a wave. Different wavelengths correspond to different types of electromagnetic radiation, from radio waves to gamma rays.
Frequency (f):The number of wave cycles passing a point per unit time. Frequency and wavelength are inversely related: \(f = \frac{c}{λ}\), where \(c\) is the speed of light (\(3 \times 10^8\) m/s in a vacuum).
Speed:In a vacuum, all electromagnetic waves travel at the speed of light (\(c\)), regardless of their frequency or wavelength.

Real Life Application

One real-life application of electromagnetic waves is in RFID (Radio Frequency Identification) technology. RFID systems use electromagnetic waves to wirelessly identify and track objects, animals, or people. For example, in retail stores, RFID tags are attached to products for inventory management and anti-theft purposes. When a tagged item passes through a reader's electromagnetic field at the store's entrance or exit, the tag emits a unique radio signal containing product information. The reader captures this signal, allowing the store to track inventory in real-time and prevent shoplifting. RFID technology is also used in transportation systems, such as toll collection on highways and public transportation fare payment. Additionally, it's employed in tracking baggage at airports, managing inventory in warehouses, and monitoring livestock in agriculture.

Example

An example of an electromagnetic wave is visible light. Visible light is the portion of the electromagnetic spectrum that human eyes can detect. It ranges from shorter wavelengths, which appear violet or blue, to longer wavelengths, which appear red. Examples of visible light include sunlight, the light emitted by light bulbs, and the colors we see in rainbows.

Uses of it

Communication: Radio waves, microwaves, and infrared waves are used for wireless communication technologies such as radio broadcasting, television broadcasting, cell phones, Wi-Fi, Bluetooth, and satellite communication.
Medical Imaging: X-rays, gamma rays, and radio waves are used in medical imaging techniques such as X-ray radiography, CT scans, MRI scans, PET scans, and fluoroscopy to diagnose and treat diseases.
Cooking: Microwaves are used in microwave ovens for cooking and heating food quickly and efficiently.
Security and Surveillance: Millimeter waves and infrared waves are used in security scanners at airports and other high-security locations to detect hidden objects on individuals and to monitor areas for intruders.

ELECTROMAGNETIC WAVE FORMULA:

c = f× λ Where:

c = speed of light (m/s)

f = frequency (Hz)

λ = wavelength (m)

It asserts that the speed of light, a universal constant denoted by c, is always equal to the product of the wavelength ( λ ) and the frequency ( f ) of the electromagnetic wave. As the wavelength increases, the frequency decreases, and vice versa, but their multiplication always equals the speed of light, which remains constant.

Frequency Formula

c = f× λ c = f× λ c = f× λ f = c

λ λ λ λ λ

Wavelength Formula

c = f× λ c = f× λ c = f× λ λ = c

f f f f f

Sample Problems

Problem 1:

A radio transmitter emits electromagnetic waves with a frequency of 100 MHz. Calculate the wavelength of these waves in meters.

Given:

Frequency (f) = 100 MHz = (100×10^6) Hz

Speed of light (c) = (3×10^8 ) m/s

Unknown:

Wavelength (λ)

Formula:

The relationship between frequency, wavelength, and the speed of light is given by the equation:

c= f× λ

Solution:

Substitute the given values into the formula:

λ = c

λ = 3m

Answer:

The wavelength of the electromagnetic waves emitted by the radio transmitter is 3 meters.

Explanation (Radio Waves):

Consider radio waves as little waves moving across space. According to the issue, radio waves vibrate at a frequency of 100 million times per second, or 100 MHz. We are interested in the wavelength, or the distance, between these waves. According to a formula we utilize, the speed of light is equal to the frequency (the rate at which waves vibrate) times the wavelength (the distance between them). We may determine the wavelength to be 3 meters by rearranging the equations.

Problem 2:

An electromagnetic wave has a wavelength of 500 nm. Calculate its frequency.

Given:

Wavelength (λ) = 500 nm = (500×10^9 ) m

Speed of light (c) = (3×10^8 ) m/s

Unknown:

Frequency (f)

Formula:

Use the same formula as in Problem 1: c= f× λ

Solution:

Rearrange the formula to solve for frequency:

f= c

f= 6×10^14 Hz

Answer:

The frequency of the electromagnetic wave is (6×10^14 ) Hz

Explanation (Light Waves):

Let us now consider another type of electromagnetic wave, such as light. It is stated that the wavelength of this light is 500 billionths of a meter, or 500 nm. Since light moves at a very high speed, we can calculate its frequency—or how quickly it vibrates—using the same formula. We calculate the frequency of vibration by entering in the values and find that it is 600 trillion times per second (600 THz).

Sample Problems With Correct Answer

PROBLEM 1:

The frequency of an visible light is 5×10^14 Hz. Given that light moves at a speed of 3×10^8m/s in a vacuum, find the wavelength in meters.

Identify the given in the problem, wherein:

Frequency (f) = 5×10^14 Hz

Speed of light (c) = 3×10^8m/s

Unknown: Wavelength (λ)= ?

Formula: c= f × λ

By rearranging the equation for the speed of light to solve for wavelength, we can plug in the given values to find the wavelength.

c = f × λ

f f

λ= c

Solution:

Subsitute the given values in the formula

λ= c

λ= 3×10^8 m/s

5×10^14 Hz

λ= 6×10meters

Answer:

The wavelength of the visible light is 6×10 meters

PROBLEM 2:

An electromagnetic wave traveling in a speed of 3×〖10〗^8meters per second and a wavelength of 3×10^-2 meters. What is its frequency?

Given:

Wavelength(λ)= 3×10^-2 meters

Speed of light (c) = 3×10^8 m/s

Unknown: Frequency (f)=?

Formula: c= f × λ

We rearrange the equation to solve for frequency

c = f × λ

c = f ×λ

λ λ

f = c

Solution:

Substitute the given values in the formula

f = c

f = 3×10^8 m/s

3×10^-2 m

f = 3×10^8 m/s

3×10^-2 m

f = 1×10^9 Hz

Answer:

The frequency of the electromagnetic wave is 1×10^9 Hz

SUMMARY

Electromagnetic waves or EM waves are form of waves that travels through the universe. An accelerating charged particle generates the electromagnetic field. EM waves are nothing but electric and magnetic fields traveling through free space at the speed of light. There are three properties of EM waves, namely: Wavelength, Frequency and Speed.

These type of waves are included in the electromagnetic spectrum which encompasses the entire range of electromagnetic waves such as radiowaves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. This spectrum has 4 types of behavior such as reflection, refraction, diffraction and interference.

EM waves are used in various ways, most dominantly in technology. These are used in the medical field for detecting and diagnosing diseases such as the x-rays, CT scans and MRI and PET scans. Additionally, these waves can also be used for communication, security and surveillance, cooking and many more.

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