Electromagnetic Waves - Definition, Mathematical Representation, Equation, Electromagnetic Spectrum, FAQs

Electromagnetic Waves - Definition, Mathematical Representation, Equation, Electromagnetic Spectrum, FAQs

Edited By Team Careers360 | Updated on Jul 02, 2025 05:02 PM IST

In Physics, the abbreviation EM or EM meaning is given as Electromagnetic Waves. Electromagnetic waves are discovered by the physicist Heinrich Hertz experimentally and the basic idea of EM wave definition is taken from the Maxwell electromagnetic wave theory and as a result of Maxwell equations, Electromagnetic waves are considered to be the fundamental of the electrodynamics subject. In this article, let us see an introduction to electromagnetic waves, em theory, energy of em waves, and try to understand what are electromagnetic waves, what is the graphical representation of em waves and what these electromagnetic waves produce with some electromagnetic waves examples.

Electromagnetic Waves - Definition, Mathematical Representation, Equation, Electromagnetic Spectrum, FAQs
Electromagnetic Waves - Definition, Mathematical Representation, Equation, Electromagnetic Spectrum, FAQs

What are Electromagnetic Waves?

According to electromagnetic theory, electromagnetic waves definition is given as the waves which are formed due to the vibrations created between the Electric and Magnetic field. In short, Electromagnetic waves are composed of an oscillating electric field and a magnetic field. In a vacuum, the velocity of electromagnetic waves is calculated to be 3.00×108m/s (which is also the velocity of light). Electromagnetic waves travel through space at the speed of light. The velocity of an electromagnetic wave in the medium is given by the equation $\mathrm{V}=\frac{\mathrm{c}}{\mathrm{n}}$, where c is the velocity of light and n is the refractive index of the respective medium.

How are Electromagnetic Waves Produced?

When Electric fields are produced by any charged particles, some kind of force is exerted on the other nearest charged particle by the electric field. The charges which are positive in nature will accelerate along the direction of the electric field and the charges which are negative in nature will accelerate along the opposite direction of the electric wave field. At the same time, it is observed that the magnetic wave field is produced by the moving charges. The magnetic field exerts a force on other nearby moving charges and this force is always exerted perpendicular to the direction of their own velocities. (Note: only velocity should be considered here, not the speed of the particles). Thus the generation of Electromagnetic waves is due to the effect of some accelerating charged particles.

In an electromagnetic wave, the electric and magnetic fields are found to be perpendicular to the electromagnetic waves. An Electromagnetic wave can be assumed as the combined electric and magnetic field which propagates through free space with light speed. This oscillation of the charged particle has some frequency f and thus the resultant EM waves will also form with the same frequency f. Let us consider the wavelength of the Em waves is λ, then λ is given by =c/f where C denotes the velocity of light and f denotes the frequency of the EM wave. Thus the source of the Electromagnetic waves is the charged particles which are accelerated. In simple words, the production of electromagnetic waves is due to oscillating charged particles. Hope, now it is clear how electromagnetic waves are produced by oscillating charges or accelerated charged particles.

NEET Highest Scoring Chapters & Topics
This ebook serves as a valuable study guide for NEET exams, specifically designed to assist students in light of recent changes and the removal of certain topics from the NEET exam.
Download E-book

A graphical representation of the EM waves is given in the following diagram:

The blue wave represents the electric field E and the red wave represents the magnetic field and the direction of propagation is perpendicular to E and B.

From the above-depicted image, The electric and magnetic fields of an electromagnetic wave are denoted by blue and red colour waves. It is found that the electric and magnetic fields themselves are perpendicular to each other and also perpendicular direction of electromagnetic wave propagation. If the electric field is in the x direction and the magnetic field is in the y direction, then the direction of propagation of the electromagnetic wave is given by perpendicular direction to both x and y direction i.e in the z direction. The direction of an em wave changes when the direction of the electric and magnetic field changes.

Mathematical Representation of EM Wave

Let us take a plane electromagnetic wave which travels in the direction of the x. Now, The electric field of an electromagnetic wave is given by $E(x, t)=E m a x i m u m c o s(k x-\omega t+\phi)$ and the magnetic field of an electromagnetic wave is given by $B(x, t)=\mathrm{B}_{\text {maximum }} \cos (k x-\omega t+\phi)$.

Em wave equation for the respective electric and magnetic field in a plane electromagnetic wave is given by $\vec{E} \times \vec{B}$, and the velocity of the electromagnetic wave is parallel to $\vec{E} \times \vec{B}$.

where E denotes the electric field vector and B denotes the magnetic field vector.

According to Maxwell's electromagnetic wave theory of light, the electromagnetic wave formula is given by

$\begin{aligned} & \nabla \cdot \mathrm{E}=0 \\ & \nabla \cdot \mathrm{~B}=0 \\ & \Delta \times E=-\frac{\partial B}{\partial t} \\ & \Delta \times E=-\frac{\partial E}{\partial t} \mu \varepsilon\end{aligned}$

Electromagnetic Wave Equation Derivation

The Electromagnetic wave equation gives the propagation of Em waves in a medium or vacuum. It is a second-order partial differential equation and also it takes the wave equation in 3d form.

The homogeneous form of the electromagnetic rays is given by

$$
\begin{aligned}
& \frac{\partial B}{\partial x^2} \mu \varepsilon-\frac{\partial B}{\partial t^2}=0 \\
& \frac{\partial E}{\partial x^2} \mu \varepsilon-\frac{\partial E}{\partial t^2}=0
\end{aligned}
$$
Where $\mu=$ permeability in medium or free space $\varepsilon=$ permittivity in medium or free space

The intensity of EM Wave

Let us consider the electromagnetic waves that transport in free space Now, the intensity of electromagnetic waves I can be written as

$$
I=\frac{P}{A}=\frac{1}{2} C \varepsilon_0 E^2=\frac{1}{2} \frac{c}{\mu_0} \varepsilon_0 E^2
$$
The above equation gives the intensity of the electromagnetic wave equation in free space.
Where $\mu_0=$ permeability in free space
$\varepsilon_0=$ permittivity in free space
$\mathrm{C}=$ velocity of light (velocity of an electromagnetic wave in free space $=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ )

Electromagnetic Spectrum

In a plane, electromagnetic waves travel in free space and are classified according to their individual frequency or their respective wavelengths. This wavelength differs from one light to the other. For example,

  • The Wavelength of Visible light will be around from 400 nm to 700 ni
  • The Wavelength of violet light will be around from approx 400 nm
  • The Wavelength of red light will be around from approx 700 nm

Also read -

Application of Electromagnetic waves

There are plenty of applications of electromagnetic theory and electromagnetic waves in practice. Let us discuss a few of the applications for electromagnetic waves below:

  • The electromagnetic signal are used to transmit energy in free space

  • We can also find the application of the em waves in communication.

  • Electromagnetic fields and waves are also used in RADAR applications.

  • UV rays which are considered to be em waves are used in the detection of forged documents.

  • IR rays are used for night cameras and security cameras.

Frequently Asked Questions (FAQs)

1. What is em and what are em waves? OR what's an electromagnetic wave?

    The EM waves can expand as Electromagnetic waves. These waves are formed due electromagnetic effects caused by oscillating charged particles. These waves are the result of an electric and magnetic wave combination.

2. What is electromagnetic theory?

    The electromagnetic theory is proposed by Maxwell and this theory tells that electric flux in a closed surface is proportional to the charge enclosed by the closed surface and the magnetic flux in a closed surface is considered to be zero.

3. How to make electromagnetic waves and how an electromagnetic wave is produced?

The electromagnetic waves are produced when the charged particles oscillate. The accelerated charged particles produce the Em waves.

4. Is light an electromagnetic wave?

The answer for this question is YES. One of the best examples of em waves is light waves.The electromagnetic waves travel with the speed of light. The light waves are composed of both electric and magnetic parts.

5. Do electromagnetic waves carry energy and momentum?

Yes, the Em waves are eligible to carry energy E and Momentum p. Thus, Em waves can transfer energy through the free space.

6. What are the sources of electromagnetic waves? ( ncert class 12)

The source of em waves is accelerated charged particles. In a plane em wave, the electric field oscillates sinusoidally.

7. What is the electromagnetic spectrum?
The electromagnetic spectrum is the complete range of all types of electromagnetic radiation, arranged according to their frequencies or wavelengths. It includes, from lowest to highest frequency: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. All these types of radiation are fundamentally the same, differing only in their frequencies and energies.
8. How does the energy of an electromagnetic wave relate to its frequency?
The energy of an electromagnetic wave is directly proportional to its frequency. This relationship is described by the equation E = hf, where E is the energy of a photon (the particle aspect of the wave), h is Planck's constant, and f is the frequency of the wave. Higher frequency waves have more energy, which is why gamma rays are more energetic and potentially harmful than radio waves.
9. What is the speed of electromagnetic waves in vacuum?
All electromagnetic waves travel at the same speed in vacuum, which is the speed of light, approximately 3 x 10⁸ m/s. This speed is often denoted by the symbol c. In media other than vacuum, electromagnetic waves travel slower, and their speed depends on the properties of the medium.
10. How are wavelength, frequency, and speed of an electromagnetic wave related?
The wavelength (λ), frequency (f), and speed (c) of an electromagnetic wave are related by the equation c = λf. This means that for a given speed (which is constant in vacuum), as the frequency increases, the wavelength decreases, and vice versa. This relationship explains why high-frequency waves like gamma rays have very short wavelengths, while low-frequency waves like radio waves have long wavelengths.
11. How do electromagnetic waves interact with matter?
Electromagnetic waves can interact with matter in several ways:
12. What are electromagnetic waves?
Electromagnetic waves are self-propagating oscillations of electric and magnetic fields that travel through space at the speed of light. They don't require a medium to travel and can propagate through a vacuum. These waves carry energy and momentum, and are responsible for various phenomena like light, radio waves, and X-rays.
13. What is the relationship between the electric and magnetic fields in an electromagnetic wave?
In an electromagnetic wave, the electric and magnetic fields are perpendicular to each other and to the direction of wave propagation. They oscillate in phase, meaning they reach their maximum and minimum values at the same time. The magnitudes of the electric and magnetic fields are related by the equation E = cB, where c is the speed of light in vacuum.
14. What is the difference between transverse and longitudinal waves, and which type are electromagnetic waves?
Transverse waves oscillate perpendicular to their direction of travel, while longitudinal waves oscillate parallel to their direction of travel. Electromagnetic waves are transverse waves. Both the electric and magnetic field components oscillate perpendicular to the direction of wave propagation, making them transverse waves.
15. How are electromagnetic waves mathematically represented?
Electromagnetic waves are typically represented by sinusoidal functions. The electric and magnetic field components are perpendicular to each other and to the direction of wave propagation. The general form of an electromagnetic wave traveling in the x-direction can be written as:
16. What is polarization of electromagnetic waves?
Polarization refers to the orientation of the electric field oscillations in an electromagnetic wave. In a linearly polarized wave, the electric field oscillates in a single plane perpendicular to the direction of propagation. Circular and elliptical polarizations are also possible, where the direction of the electric field rotates as the wave propagates. Polarization is important in many applications, including LCD screens and polarized sunglasses.
17. How do electromagnetic waves behave in superconductors?
Superconductors interact with electromagnetic waves in unique ways:
18. How do electromagnetic waves carry energy and information?
Electromagnetic waves carry energy through the oscillations of their electric and magnetic fields. The amount of energy is related to the wave's frequency and amplitude. They carry information through modulation - variations in the wave's amplitude, frequency, or phase. For example, in radio broadcasting, the sound information is encoded into variations of the carrier wave's amplitude or frequency.
19. What is the photoelectric effect and how does it relate to electromagnetic waves?
The photoelectric effect is the emission of electrons from a material when it's exposed to light (electromagnetic radiation). It demonstrates the particle nature of light, as the effect depends on the frequency of the light, not its intensity. This phenomenon is explained by treating light as discrete packets of energy called photons, where each photon's energy is given by E = hf, linking the wave (frequency) and particle (energy) aspects of electromagnetic radiation.
20. How do electromagnetic waves propagate in a vacuum?
Electromagnetic waves can propagate in a vacuum because they don't require a medium. The oscillating electric field creates a changing magnetic field, which in turn creates a changing electric field, and so on. This self-sustaining process allows the wave to propagate through empty space at the speed of light. This is unlike mechanical waves, such as sound, which require a medium to travel.
21. What is the significance of Maxwell's equations in understanding electromagnetic waves?
Maxwell's equations are a set of four fundamental equations that describe how electric and magnetic fields are generated and interact. They predict the existence of electromagnetic waves and show that light is an electromagnetic wave. These equations unify electricity, magnetism, and optics into a single theory, demonstrating that changing electric fields produce magnetic fields and vice versa, which is the basis for electromagnetic wave propagation.
22. How do electromagnetic waves behave when they encounter a boundary between two media?
When electromagnetic waves encounter a boundary between two media:
23. What is the Doppler effect for electromagnetic waves?
The Doppler effect for electromagnetic waves is the change in observed frequency when there is relative motion between the source of the waves and the observer. If the source is moving towards the observer, the observed frequency is higher than the emitted frequency (blueshift). If the source is moving away, the observed frequency is lower (redshift). This effect is used in astronomy to measure the velocities of distant galaxies and in radar systems to measure the speed of moving objects.
24. How does the intensity of electromagnetic radiation change with distance from the source?
The intensity of electromagnetic radiation decreases with the square of the distance from the source. This is known as the inverse square law. Mathematically, I ∝ 1/r², where I is the intensity and r is the distance from the source. This occurs because the energy of the wave spreads out over an ever-increasing area as it travels away from the source, resulting in less energy per unit area at greater distances.
25. What is electromagnetic interference (EMI) and how does it occur?
Electromagnetic interference (EMI) is the disruption of the operation of an electronic device when it's in the vicinity of an electromagnetic field caused by another device. It occurs when electromagnetic waves from one source interact with electrical systems or other electromagnetic waves, causing unwanted effects. EMI can be caused by both natural sources (like lightning) and man-made sources (like motors or cell phones). Managing EMI is crucial in electronic design and in maintaining the proper function of sensitive equipment.
26. How do antennas work with electromagnetic waves?
Antennas are devices designed to transmit or receive electromagnetic waves. For transmission, an antenna converts electrical energy into electromagnetic waves that radiate into space. For reception, it captures electromagnetic waves and converts them back into electrical signals. The size and shape of an antenna are related to the wavelength of the electromagnetic waves it's designed to work with. Antennas can be designed to be omnidirectional (radiating or receiving equally in all directions) or directional (focusing energy in specific directions).
27. What is the relationship between electromagnetic waves and photons?
Electromagnetic waves exhibit both wave-like and particle-like properties, a concept known as wave-particle duality. Photons are the particle aspect of electromagnetic radiation. Each photon carries a discrete amount of energy E = hf, where h is Planck's constant and f is the frequency of the associated electromagnetic wave. The wave aspect describes how the electromagnetic radiation propagates through space, while the particle aspect (photons) is useful for understanding how the radiation interacts with matter, such as in the photoelectric effect.
28. How do electromagnetic waves interact with charged particles?
Electromagnetic waves can interact strongly with charged particles. When an electromagnetic wave encounters a charged particle:
29. What is the difference between near-field and far-field regions of electromagnetic radiation?
The near-field and far-field are two regions of electromagnetic radiation around a transmitting antenna:
30. How do electromagnetic waves behave in conductors versus insulators?
The behavior of electromagnetic waves in conductors and insulators is quite different:
31. What is the significance of the electric and magnetic field components being in phase in an electromagnetic wave?
The electric and magnetic field components of an electromagnetic wave being in phase is significant because:
32. How does the concept of electromagnetic waves relate to the principle of electromagnetic induction?
Electromagnetic induction and electromagnetic waves are closely related concepts:
33. What is the role of electromagnetic waves in the greenhouse effect?
Electromagnetic waves play a crucial role in the greenhouse effect:
34. How do electromagnetic waves behave in plasmas?
Plasmas, which are ionized gases, interact with electromagnetic waves in complex ways:
35. What is the relationship between electromagnetic waves and the special theory of relativity?
Electromagnetic waves and special relativity are deeply connected:
36. How do electromagnetic waves interact with dielectric materials?
When electromagnetic waves interact with dielectric materials:
37. What is the significance of the electric and magnetic field amplitudes being perpendicular in electromagnetic waves?
The perpendicular orientation of electric and magnetic fields in electromagnetic waves is significant because:
38. How do electromagnetic waves behave in metamaterials?
Metamaterials are artificially engineered materials that can manipulate electromagnetic waves in ways not found in nature:
39. What is the role of electromagnetic waves in quantum electrodynamics (QED)?
In quantum electrodynamics (QED), electromagnetic waves are described in terms of photons, the quantum of the electromagnetic field:

Articles

Back to top