Electromagnetic Waves - Notes, Topics, Types, Formulas, Books, FAQs

Important Topics of Electromagnetic Waves

Chapter Electromagnetic Waves describes the nature of energy propagated in space in the form of coupled electric and magnetic fields. Among the significant ones are the origin, nature, properties and classification of electromagnetic waves and their extensive applications. These topics have to be understood well in Class 12 board exams, JEE and NEET because most questions are concept-based and NCERT-based.

1. Displacement Current

Displacement Current is a concept introduced by Maxwell to discuss the way an electric field that varies with time can be used to generate a magnetic field even in places where there is no actual flow of charge. This topic describes the reason the magnetic field exists between the plates of a charging capacitor, in which conduction current does not take place. It points to the necessity of adjusting the circuital law of Ampere so as to ensure continuity of current under any circumstance. The phenomenon of displacement current is critical to an explanation of the cause and spread of electromagnetic waves.

2. Maxwell's Equations

The Equations of Maxwell are the basic laws which explain the behaviour and interaction of magnetic and electric fields. This topic describes the way that electric charges and currents give rise to the electric and magnetic fields, and how varying electric fields create magnetic fields and vice versa. It unites the laws of electrostatics, magnetostatics and electromagnetic induction into a single system. Theoretical knowledge of Maxwell equations is crucial in explaining the origin of electromagnetic waves and is the theoretical basis of classical electromagnetism.

3. Nature of Electromagnetic Waves

The electromagnetic waves make it possible to understand how energy travels through space as vibrating magnetic and electric fields. These are perpendicular to each other and to the direction of wave propagation, and support one another without a medium of material. Electromagnetic waves are transverse waves that pass in free space at a speed equal to that of light. It is imperative to understand their nature to explain the electromagnetic spectrum and the origin of electromagnetic radiation.

4. Electromagnetic Spectrum

The electromagnetic spectrum can be defined as the entire set of electromagnetic waves that are organised based on their wavelengths or frequencies. The subject describes the property of electromagnetic radiation that extends between radio waves with long wavelengths and gamma rays with very short wavelengths, including microwaves, infrared, visible light, ultraviolet, and X-rays. It also provides the property characteristics and relative positions of each region in the spectrum. The electromagnetic spectrum is crucial to comprehend in order to associate the electromagnetic waves with their real-life use in communication, medicine, astronomy, and technology.

5. Energy and Momentum of Electromagnetic Waves

According to Energy and Momentum of Electromagnetic Waves, electromagnetic waves can have energy and momentum since they can propagate through space. This subject explains the process of transfer of energy by electromagnetic radiation and the way in which this radiation can apply a force (radiation pressure) to matter. It emphasises the physical importance of electromagnetic waves in addition to wave propagation. This concept is significant in explaining matters like the solar radiation pressure and energy transfer in communication systems.

Important Formulas of Electromagnetic Waves

Fundamental Formulae of Electromagnetic Waves are the most important mathematical formulae applied to explain the behaviour and propagation of electromagnetic radiation, energy transfer, and the effects of electromagnetic radiation on matter. These equations assist in the comprehension of the connection between the electric and magnet field as well as the speed of the electromagnetic wave and the energy and momentum that the waves bear. It is also significant to revise and appropriately apply these formulas on a regular basis in solving conceptual and numerical problems in Class 12 board exams and competitive exams such as JEE Main and NEET.

1. Speed of electromagnetic waves in vacuum:

$
c=\frac{1}{\sqrt{\mu_0 \varepsilon_0}}
$

where
$\mu_0=$ permeability of free space
$\varepsilon_0=$ permittivity of free space

2. Relation Between Electric and Magnetic Fields:

E=cB

3. Wave speed relation:

$
c=\lambda f
$

where
$\lambda=$ wavelength
$f=$ frequency

4. Energy in Electromagnetic Waves:

Energy density of an electromagnetic wave

$
u=\frac{1}{4} \varepsilon_0 E_o^2+\frac{1}{4} \frac{B_o^2}{\mu_0}
$
Average energy density

$
u=\frac{1}{2}\varepsilon_0 E^2
$

5. Momentum of Electromagnetic Waves:

$p=\frac{u}{c}$

7. Radiation Pressure:

• Radiation pressure on a perfectly absorbing surface

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

• Radiation pressure on a perfectly reflecting surface

$
P=\frac{2 I}{c}
$
Where I is the intensity of electromagnetic radiation.

Electromagnetic Waves: Previous Year Questions

Past Years' Questions on Electromagnetic Waves enable the students to get familiar with the nature and structure of the questions that are often discussed in examinations of this chapter. These tests are primarily based on the conceptualisation of the idea of displacement current, nature of electromagnetic waves, electromagnetic spectrum and their uses according to NCERT. PYQs practice sharpens the understanding of concepts and is particularly applicable in getting good scores in Class 12 board exams, JEE Main and NEET.

Question 1:

A plane electromagnetic wave of wave intensity $6 \mathrm{~W} / \mathrm{m}^2$ strikes a small mirror area $40 \mathrm{~cm}^2$, held perpendicular to the approaching wave. The momentum transferred by the wave to the mirror each second will be:

Solution:

Momentum transferred in one second

$
\begin{aligned}
& P=\frac{2 U}{c}=\frac{2 S_{a v} A}{c} \\
& =\frac{2 \times 6 \times 40 \times 10^4}{3 \times 10^8} \\
& =1.6 \times 10^{-10} \mathrm{~kg}-\mathrm{m} / \mathrm{s}^2
\end{aligned}
$

Question 2:

The magnetic field of a plane electromagnetic wave is given by $\vec{B}=B_0 \hat{i}[\cos (k z-\omega t)]+ B_1 \hat{j} \cos (k z+\omega t)$, where $B_0=3 \times 10^{-5} \mathrm{~T}$ and $B_1=2 \times 10^{-6} \mathrm{~T}$. The RMS value of the force experienced by a stationary charge $Q=10^{-4} C$ at $z=0$ is closest to:

Solution:

$
\begin{aligned}
& \vec{B}=B_0 \hat{i}[\cos (k z-\omega t)]+B_1 \hat{j} \cos (k z+\omega t) \\
& B_0=3 \times 10^{-5} T B_1=2 \times 10^{-6} T
\end{aligned}
$
Electric filed associated with it is,

$
\vec{E}=-B_0 c \hat{j} \cos (k z-\omega t)-B_1 \hat{c i} \cos (k z+\omega t)
$
Here, c is the speed of light in a vacuum.
At $z=0$,

$
F_{\mathrm{rms}}=\sqrt{\frac{\left(Q B_0 c\right)^2+\left(Q B_1 c\right)^2}{2}}
$
Here $c$ is the speed of light in vacuum.

$
\begin{aligned}
& =\sqrt{\frac{\left((10)^{-4} \times 3 \times(10)^{-5} \times 3 \times(10)^8\right)^2+\left((10)^{-4} \times 2 \times(10)^{-6} \times 3 \times(10)^8\right)^2}{2}} \\
& =\sqrt{\frac{0.81+0.0036}{2}}=0.6 \mathrm{~N}
\end{aligned}
$

Question 3:

The peak electric field produced by the radiation coming from the 8 W bulb at a distance of 10 m is $\frac{x}{10} \sqrt{\frac{\mu_0 c}{\pi}} \frac{V}{m}$. The efficiency of the bulb is $10 \%$, and it is a point source. The value of $x$ is $\_\_\_\_$ .

Solution:

Given: Power, $\mathrm{P}=8 \mathrm{~W}$
distance, $\mathrm{r}=10 \mathrm{~m}$
As we know that the intensity is $\mathrm{I}=\frac{1}{2} c \epsilon_o E_o^2$ and also it is written as, $\mathrm{I}=\frac{P}{A}$

Here the area is written as, $\mathrm{A}=4 \pi r^2$
Now, by putting all the given values we have;

$
\begin{aligned}
& \Rightarrow \mathrm{I}=\frac{8}{4 \pi r^2}=\frac{2}{\pi r^2} \\
& \Rightarrow \frac{1}{2} c \epsilon_o E_o^2=\frac{2}{\pi r^2}
\end{aligned}
$
Here we have $\epsilon_o=\frac{1}{\mu_o c^2}$

$
\begin{aligned}
& \Rightarrow \frac{1}{2} c \times \frac{1}{\mu_o c^2} E_o^2=\frac{2}{\pi \times 10^2} \\
& \Rightarrow E_o^2=\frac{4 \mu_o c}{\pi \times 10^2} \\
& \Rightarrow E_o=\frac{2}{10} \sqrt{\frac{c \mu_o}{\pi}}
\end{aligned}
$
Therefore the value of $\mathbf{x}$ is $\mathbf{2}$

Electromagnetic Waves in Different Exams

Electromagnetic Waves is a concept-based chapter in Class 12 Physics that dwells upon the origin, nature, and uses of electromagnetic radiation. This chapter mostly contains theory-based and NCERT-oriented questions, and thus, it is a scoring topic in most exams. The knowledge of the exam-wise concentration areas and weightage assists the students to study smartly and eliminate any redundancy in depth where not needed.

Important Books and Resources for Class 12 Electromagnetic Waves

In order to master the chapter Electromagnetic Waves, one must use a combination of NCERT textbooks, reference guides and practice materials explaining the basic ideas as well as their practical implementation. These materials can be used to understand the concepts of displacement current, Maxwell's ideas, electromagnetic spectrum, wave properties, and transport of energy, which are a vital requirement in Class 12 board exams and competitive exams such as JEE Main, JEE Advanced and NEET.

NCERT Resources for Electromagnetic Waves

The most significant and valuable study materials in this chapter are the NCERT resources on Electromagnetic Waves because the information in the chapter is very NCERT-centric in board and competitive exams. The NCERT textbook and the exemplar problems cover the concepts of displacement current, nature of electromagnetic waves, electromagnetic spectrum and their applications in a simple and succinct manner. Comprehensive reading of NCERT books is critical in achieving good scores in Class 12 board exams, NEET and JEE Main, where most of the questions are either direct or indirectly based on NCERT theory and definitions.

• NCERT solutions for Class 12 Physics Chapter 8 Electromagnetic Waves
• NCERT notes Class 12 Physics Chapter 8 Electromagnetic Waves
• NCERT Exemplar Class 12 Physics Solutions Chapter 8

NCERT Subjectwise Resources

NCERT subject-wise materials are organised and syllabus-based learning content on various subjects, which assists students in developing a good conceptual basis. They consist of textbooks, exemplar problems, and solutions and can thus be very helpful in the preparation for the board exams and even competitive exams such as JEE and NEET.

Practice Questions based on Electromagnetic Waves

Practice Problems about Electromagnetic Waves will reinforce the students on how electromagnetic radiation is created, spreads and acts on matter. The questions are primarily related to displacement current, nature of EM waves, electromagnetic spectrum, energy and momentum of EM waves and applications in real life. Students can recall NCERT facts more easily and develop conceptual clarity, and are well prepared to take Class 12 board exams, NEET, and JEE Main, where this chapter is mostly theory-based and scoring.

Conclusion

These concepts are presented well in the chapter Electromagnetic Waves, giving a conceptual framework for understanding how energy travels through space in the form of coupled electric and magnetic fields. Through continuous revision of fundamental concepts, relevant definitions and material relations pertaining to displacement current, nature of waves, electromagnetic spectrum and usability, the student can gain a good conceptual clarity. This is very effective in building confidence and is very much required to produce good results in the Class 12 board exam, as well as competitive exams such as JEE Main and NEET.

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