Physics · Class 12 Science
Ch 8Electromagnetic Waves — Class 12 Physics, concept-first.
By this point in the course, two results are already familiar:
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Electromagnetic Wave Relation
Imagine you're standing at the beach. You see a wave coming in — it has a certain speed, a certain distance between crests (wavelength), and a certain number of crests passing you per second (frequency).
Most relevant Q&A
- A plane electromagnetic wave of frequency $25\ \text{MHz}$ travels in free space along the $x$-direction. At a particular point in space and…Free
- The magnetic field in a plane electromagnetic wave is given by $B_y = (2 \times 10^{-7})\ \text{T} \sin (0.5\times10^{3}x + 1.5\times10^{11}…Preview
- A plane electromagnetic wave travels in vacuum along $z$-direction. What can you say about the directions of its electric and magnetic field…Preview
- A radio can tune in to any station in the $7.5\ \text{MHz}$ to $12\ \text{MHz}$ band. What is the corresponding wavelength band?Preview
- The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is $B_0 = 510\ \text{nT}$. What is the amplitude of th…Preview
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
By this point in the course, two results are already familiar:
Displacement Current
Ampere's circuital law (from Chapter 4) states that the line integral of the magnetic field around a closed loop is proportional to the current passing through any surface bounded by that loop:
Electromagnetic Waves
Electromagnetic waves are self-sustaining oscillations of electric and magnetic fields that travel through space at the speed of light.
Sources of Electromagnetic Waves
Electromagnetic waves are not produced by every charge. The key condition is acceleration.
Nature of Electromagnetic Waves
Electromagnetic waves are self-sustaining oscillations of electric and magnetic fields. From Maxwell’s equations, a key result emerges: in an electromagnetic wave, the electric field and the magnetic…
+−Worked Examplesi2 questions
- Example 8.1A plane electromagnetic wave of frequency $25\ \text{MHz}$ travels in free space along the $x$-direction. At a particular point in space and…Free
- Example 8.2The magnetic field in a plane electromagnetic wave is given by $B_y = (2 \times 10^{-7})\ \text{T} \sin (0.5\times10^{3}x + 1.5\times10^{11}…Preview
Electromagnetic Spectrum
The electromagnetic spectrum is the complete classification of all electromagnetic (EM) waves arranged by their frequency (or wavelength). At the time of Maxwell, only visible light was well-known.
Radio Waves
Radio waves are generated by the accelerated motion of charges — specifically, electrons moving back and forth in a conducting wire (like an antenna).
Microwaves
Microwaves are short-wavelength radio waves with frequencies in the gigahertz (GHz) range. They lie between radio waves and infrared in the electromagnetic spectrum.
Infrared Waves
Infrared waves are electromagnetic waves with frequencies and wavelengths that place them just below the visible spectrum — specifically, at its low-frequency (long-wavelength) end.
Visible Rays
Visible light is the only part of the electromagnetic spectrum that the human eye can detect. It is the most familiar form of EM waves because it directly carries information about the world around us…
Ultraviolet Rays
Ultraviolet (UV) rays are electromagnetic waves with wavelengths shorter than visible light but longer than X-rays. They lie just beyond the violet end of the visible spectrum.
X-rays
X-rays are a high-energy, short-wavelength region of the electromagnetic spectrum. They lie beyond the ultraviolet (UV) region, meaning they have higher frequencies and shorter wavelengths than UV ray…
Gamma Rays
Gamma rays are the highest-frequency, shortest-wavelength electromagnetic waves. They occupy the extreme upper end of the electromagnetic spectrum.
Summary
- Maxwell’s displacement current: The term added to Ampere’s law, where is electric flux. It ensures continuity of current and predicts electromagnetic waves.
Points to Ponder
1. The fundamental distinction among different types of electromagnetic waves is their wavelength (or frequency), because all electromagnetic waves travel through a vacuum at the same speed .
Exercises
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- 8.1Figure 8.5 shows a capacitor made of two circular plates each of radius $12\ \text{cm}$, and separated by $5.0\ \text{cm}$. The capacitor is…Free
- 8.2A parallel plate capacitor (Fig. 8.6) made of circular plates each of radius $R = 6.0\ \text{cm}$ has a capacitance $C = 100\ \text{pF}$. Th…Free
- 8.3What physical quantity is the same for X-rays of wavelength $10^{-10}\ \text{m}$, red light of wavelength $6800\ \text{Å}$ and radiowaves of…Free
- 8.4A plane electromagnetic wave travels in vacuum along $z$-direction. What can you say about the directions of its electric and magnetic field…Preview
- 8.5A radio can tune in to any station in the $7.5\ \text{MHz}$ to $12\ \text{MHz}$ band. What is the corresponding wavelength band?Preview
- 8.6A charged particle oscillates about its mean equilibrium position with a frequency of $10^{9}\ \text{Hz}$. What is the frequency of the elec…Preview
- 8.7The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is $B_0 = 510\ \text{nT}$. What is the amplitude of th…Preview
- 8.8Suppose that the electric field amplitude of an electromagnetic wave is $E_0 = 120\ \text{N/C}$ and that its frequency is $\nu = 50.0\ \text…Preview
- 8.9The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula $E = h\nu$ (for energy of a quantum…Preview
- 8.10In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of $2.0 \times 10^{10}\ \text{Hz}$ and amplitude…Preview
Exemplar Problems
Higher-order thinking / exemplar-style practice problems.
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- Q1One requires 11 eV of energy to dissociate a carbon monoxide molecule into carbon and oxygen atoms. The minimum frequency of the appropriate…Free
- Q2A linearly polarized electromagnetic wave given as $\mathbf{E} = E_0\hat{i}\cos(kz - \omega t)$ is incident normally on a perfectly reflecti…Free
- Q3Light with an energy flux of $20\ \text{W/cm}^2$ falls on a non-reflecting surface at normal incidence. If the surface has an area of $30\ \…Free
- Q4The electric field intensity produced by the radiations coming from a 100 W bulb at a 3 m distance is $E$. The electric field intensity prod…Preview
- Q5If $\mathbf{E}$ and $\mathbf{B}$ represent electric and magnetic field vectors of the electromagnetic wave, the direction of propagation of…Preview
- Q6The ratio of contributions made by the electric field and magnetic field components to the intensity of an EM wave is (a) $c : 1$ (b) $c^2 :…Preview
- Q7An EM wave radiates outwards from a dipole antenna, with $E_0$ as the amplitude of its electric field vector. The electric field $E_0$ which…Preview
- Q8Why is the orientation of the portable radio with respect to broadcasting station important?Preview
- Q9Why does microwave oven heats up a food item containing water molecules most efficiently?Preview
- Q10The charge on a parallel plate capacitor varies as $q = q_0\cos 2\pi\nu t$. The plates are very large and close together (area $= A$, separa…Preview
- Q11A variable frequency a.c. source is connected to a capacitor. How will the displacement current change with decrease in frequency?Preview
- Q12The magnetic field of a beam emerging from a filter facing a floodlight is given by $B_0 = 12 \times 10^{-8}\sin(1.20 \times 10^7 z - 3.60 \…Preview
- Q13Poynting vector $\mathbf{S}$ is defined as a vector whose magnitude is equal to the wave intensity and whose direction is along the directio…Preview
- Q14Professor C.V. Raman surprised his students by suspending freely a tiny light ball in a transparent vacuum chamber by shining a laser beam o…Preview
- Q15Show that the magnetic field $B$ at a point in between the plates of a parallel-plate capacitor during charging is $\dfrac{\mu_0\varepsilon_…Preview
- Q16Electromagnetic waves with wavelength (i) $\lambda_1$ is used in satellite communication. (ii) $\lambda_2$ is used to kill germs in water pu…Preview
- Q17Show that the average value of radiant flux density $S$ over a single period $T$ is given by $S = \dfrac{1}{2c\mu_0}E_0^2$.Preview
- Q18You are given a $2\ \mu\text{F}$ parallel plate capacitor. How would you establish an instantaneous displacement current of $1\ \text{mA}$ i…Preview
- Q19Show that the radiation pressure exerted by an EM wave of intensity $I$ on a surface kept in vacuum is $I/c$.Preview
- Q20What happens to the intensity of light from a bulb if the distance from the bulb is doubled? As a laser beam travels across the length of a…Preview
- Q21Even though an electric field $E$ exerts a force $qE$ on a charged particle yet the electric field of an EM wave does not contribute to the…Preview
- Q22An infinitely long thin wire carrying a uniform linear static charge density $\lambda$ lies along the $z$-axis. The wire is set into motion…Preview
- Q23Sea water at frequency $\nu = 4 \times 10^8\ \text{Hz}$ has permittivity $\varepsilon = 80\,\varepsilon_0$, permeability $\mu = \mu_0$ and r…Preview
- Q24A long straight cable of length $l$ is placed symmetrically along the $z$-axis and has radius $a\ (\ll l)$. The cable consists of a thin wir…Preview
- Q25A plane electromagnetic wave travelling in vacuum along the $z$-direction is given by $\mathbf{E} = E_0\sin(kz - \omega t)\,\hat{i}$ and $\m…Preview
- Q26A plane EM wave travelling along $z$-direction is described by $\mathbf{E} = E_0\sin(kz - \omega t)\hat{i}$ and $\mathbf{B} = B_0\sin(kz - \…Preview
- Q27An electromagnetic wave travels in vacuum along $z$-direction: $\mathbf{E} = (E_1\hat{i} + E_2\hat{j})\cos(kz - \omega t)$. Choose the corre…Preview
- Q28An electromagnetic wave travelling along $z$-axis is given as: $\mathbf{E} = E_0\cos(kz - \omega t)$. Choose the correct options from the fo…Preview
- Q29A plane electromagnetic wave propagating along $x$-direction can have the following pairs of $\mathbf{E}$ and $\mathbf{B}$ (a) $E_x, B_y$. (…Preview
- Q30A charged particle oscillates about its mean equilibrium position with a frequency of $10^9\ \text{Hz}$. The electromagnetic waves produced:…Preview
- Q31The source of electromagnetic waves can be a charge (a) moving with a constant velocity. (b) moving in a circular orbit. (c) at rest. (d) fa…Preview
- Q32An EM wave of intensity $I$ falls on a surface kept in vacuum and exerts radiation pressure $p$ on it. Which of the following are true? (a)…Preview
Sample & Board Papers
Sample papers and previous-year board questions for this subject.
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- Q1(a) Give one use of electromagnetic radiations obtained in nuclear disintegrations. (b) Give one example each to illustrate the situation wh…Preview
- Q2Mrs. Rajlakshmi had a sudden fall and was thereafter unable to stand straight. She was in great pain. Her daughter Rita took her to the doct…Preview