Electromagnetic waves (EM waves) are a fundamental concept in physics and play a crucial role in our everyday lives. From radio and television broadcasting to medical imaging and mobile communications, EM waves have endless applications. In this chapter, we will study the origin, properties, types, and applications of electromagnetic waves in detail. These notes are designed to help Class 12 students understand every concept clearly and prepare effectively for board exams and competitive exams.
Class 12 Physics Electromagnetic Waves – Complete Notes, Questions & Answers
What Are Electromagnetic Waves?
Electromagnetic waves are waves that consist of oscillating electric and magnetic fields, which are perpendicular to each other and to the direction of wave propagation.
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They do not require any medium for propagation.
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They travel at the speed of light (c = 3 × 10⁸ m/s) in a vacuum.
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Example: Light waves, radio waves, X-rays, etc.
Historical Background
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James Clerk Maxwell (1864): Gave the theoretical prediction of EM waves using Maxwell’s equations.
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Heinrich Hertz (1887): Experimentally demonstrated the existence of EM waves.
Maxwell’s Equations
Maxwell’s equations combine electricity and magnetism into one unified theory called electromagnetism.
The four equations are:
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Gauss’s Law for Electricity:
Electric charges produce electric fields.∇⋅E=ρϵ0\nabla \cdot E = \frac{\rho}{\epsilon_0}
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Gauss’s Law for Magnetism:
Magnetic monopoles do not exist; magnetic field lines are closed loops.∇⋅B=0\nabla \cdot B = 0
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Faraday’s Law of Induction:
A changing magnetic field produces an electric field.∇×E=−∂B∂t\nabla \times E = -\frac{\partial B}{\partial t}
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Ampere-Maxwell Law:
A changing electric field produces a magnetic field.∇×B=μ0ϵ0∂E∂t\nabla \times B = \mu_0 \epsilon_0 \frac{\partial E}{\partial t}
These equations predict the existence of electromagnetic waves.
Properties of Electromagnetic Waves
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EM waves are transverse waves.
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Electric field (E), Magnetic field (B), and direction of propagation (k) are mutually perpendicular.
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They carry energy and momentum.
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They obey the relation:
c=1μ0ϵ0c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}
Electromagnetic Spectrum
The electromagnetic spectrum is the entire range of frequencies or wavelengths of electromagnetic radiation.
Regions of the Electromagnetic Spectrum:
| Region | Wavelength Range | Frequency Range | Examples / Applications |
|---|---|---|---|
| Radio Waves | > 0.1 m | < 3 × 10⁹ Hz | Communication, Broadcasting |
| Microwaves | 0.1 m – 1 mm | 3 × 10⁹ – 3 × 10¹¹ Hz | Radar, Satellite Communication |
| Infrared Rays | 1 mm – 700 nm | 3 × 10¹¹ – 4 × 10¹⁴ Hz | Remote Controls, Thermal Imaging |
| Visible Light | 700 – 400 nm | 4 × 10¹⁴ – 7.5 × 10¹⁴ Hz | Human Vision, Optical Devices |
| Ultraviolet Rays | 400 – 10 nm | 7.5 × 10¹⁴ – 3 × 10¹⁶ Hz | Sterilization, Fluorescent Lamps |
| X-Rays | 10 – 0.01 nm | 3 × 10¹⁶ – 3 × 10¹⁹ Hz | Medical Imaging, Security Scanners |
| Gamma Rays | < 0.01 nm | > 3 × 10¹⁹ Hz | Cancer Treatment, Nuclear Reactions |
Mathematical Representation of EM Waves
An electromagnetic wave propagating in the x-direction can be represented as:
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Electric field:
E=E0sin(kx−ωt)E = E_0 \sin(kx – \omega t)
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Magnetic field:
B=B0sin(kx−ωt)B = B_0 \sin(kx – \omega t)
Where
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E0,B0E_0, B_0 are amplitudes,
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k=2πλk = \frac{2\pi}{\lambda} is the wave number,
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ω=2πf\omega = 2\pi f is the angular frequency.
Energy in Electromagnetic Waves
The total energy in EM waves is equally divided between the electric and magnetic fields.
Energy density:
u=uE+uBu = u_E + u_B
Where
uE=12ϵ0E2,uB=12μ0B2u_E = \frac{1}{2}\epsilon_0 E^2, \quad u_B = \frac{1}{2\mu_0} B^2
Poynting Vector
The Poynting vector gives the rate of energy flow per unit area:
S=1μ0(E×B)S = \frac{1}{\mu_0} (E \times B)
The direction of S is the direction of wave propagation.
Polarization of Electromagnetic Waves
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Unpolarized Light: Vibrations occur in all directions perpendicular to wave propagation.
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Polarized Light: Vibrations occur in only one direction.
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Polarization can be achieved using polaroid filters.
Applications of Electromagnetic Waves
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Radio Waves: Radio & TV broadcasting.
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Microwaves: RADAR, cooking in microwave ovens.
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Infrared Rays: Remote controls, night vision cameras.
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Visible Light: Vision, photography.
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Ultraviolet Rays: Sterilization of surgical instruments.
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X-Rays: Medical imaging, cancer treatment.
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Gamma Rays: Studying nuclear reactions, sterilizing food.
Important Formulas
| Quantity | Formula |
|---|---|
| Speed of EM wave | c=1μ0ϵ0c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} |
| Energy Density (Electric) | uE=12ϵ0E2u_E = \frac{1}{2}\epsilon_0 E^2 |
| Energy Density (Magnetic) | uB=12μ0B2u_B = \frac{1}{2\mu_0} B^2 |
| Poynting Vector | S=1μ0(E×B)S = \frac{1}{\mu_0} (E \times B) |
| Relation between E and B | E=cBE = cB |
Objective Questions on Electromagnetic Waves
Q1. The speed of electromagnetic waves in a vacuum depends on:
(a) Wavelength
(b) Frequency
(c) Amplitude
(d) None of these
Answer: The speed of electromagnetic waves in a vacuum is independent of wavelength, frequency, and amplitude. It is a fundamental constant c=3×108 m/sc = 3 \times 10^8 \, m/s. So, the correct answer is (d) None of these.
Q2. Which part of the electromagnetic spectrum is used for satellite communication?
(a) Radio waves
(b) Microwaves
(c) Infrared rays
(d) Ultraviolet rays
Answer: Microwaves have high frequency and can penetrate the atmosphere, making them suitable for satellite communication. So, the correct answer is (b) Microwaves.
Q3. The direction of propagation of an electromagnetic wave is:
(a) Parallel to E field
(b) Perpendicular to both E and B
(c) Parallel to B field
(d) Along E only
Answer: The direction of propagation of EM waves is perpendicular to both the electric (E) field and the magnetic (B) field. So, the correct answer is (b) Perpendicular to both E and B.
Q4. The SI unit of Poynting vector is:
(a) W/m²
(b) N/m²
(c) J/m²
(d) None of these
Answer: The Poynting vector represents power per unit area; its SI unit is watts per square meter. So, the correct answer is (a) W/m².
Q5. Infrared waves are used in:
(a) Cooking
(b) Remote controls
(c) Medical imaging
(d) Water purification
Answer: Infrared waves are commonly used in TV remotes and thermal imaging cameras. So, the correct answer is (b) Remote controls.
Q6. Which scientist experimentally demonstrated electromagnetic waves?
(a) Maxwell
(b) Hertz
(c) Newton
(d) Faraday
Answer: Heinrich Hertz experimentally demonstrated the existence of EM waves in 1887. So, the correct answer is (b) Hertz.
Q7. The relation between the electric field E and magnetic field B in free space is:
(a) E=cBE = cB
(b) E=B/cE = B/c
(c) E=BE = B
(d) E=0E = 0
Answer: In free space, the electric and magnetic fields are related by E=cBE = cB. So, the correct answer is (a) E=cBE = cB.
Q8. Electromagnetic waves transport:
(a) Only energy
(b) Only momentum
(c) Both energy and momentum
(d) Neither energy nor momentum
Answer: EM waves carry both energy and momentum because they exert radiation pressure. So, the correct answer is (c) Both energy and momentum.
Q9. Ultraviolet radiation has a wavelength range of:
(a) 400 – 700 nm
(b) 400 – 10 nm
(c) 1 mm – 700 nm
(d) < 0.01 nm
Answer: Ultraviolet radiation lies between 400 – 10 nm in the electromagnetic spectrum. So, the correct answer is (b) 400 – 10 nm.
Q10. Which law states that a changing magnetic field produces an electric field?
(a) Gauss’s Law
(b) Faraday’s Law
(c) Ampere’s Law
(d) Coulomb’s Law
Answer: Faraday’s Law of electromagnetic induction states that a changing magnetic field produces an electric field. So, the correct answer is (b) Faraday’s Law.
Q11. The speed of EM waves in a medium is given by:
(a) v=1μϵv = \frac{1}{\sqrt{\mu \epsilon}}
(b) v=μϵv = \mu \epsilon
(c) v=μ/ϵv = \sqrt{\mu / \epsilon}
(d) v=ϵ/μv = \epsilon / \mu
Answer: The speed of EM waves in a medium is v=1μϵv = \frac{1}{\sqrt{\mu \epsilon}}. So, the correct answer is (a).
Q12. The energy density of the electric field in EM waves is:
(a) 12ϵ0E2\frac{1}{2}\epsilon_0 E^2
(b) 12μ0B2\frac{1}{2\mu_0} B^2
(c) 12ϵ0B2\frac{1}{2}\epsilon_0 B^2
(d) 12μ0E2\frac{1}{2\mu_0} E^2
Answer: The energy density of the electric field is 12ϵ0E2\frac{1}{2}\epsilon_0 E^2. So, the correct answer is (a).
Q13. Gamma rays are produced during:
(a) Chemical reactions
(b) Nuclear reactions
(c) Thermal radiation
(d) Electric discharge
Answer: Gamma rays are produced in nuclear reactions and radioactive decay processes. So, the correct answer is (b) Nuclear reactions.
Q14. Which electromagnetic wave is used in medical imaging?
(a) X-rays
(b) Infrared rays
(c) Microwaves
(d) Radio waves
Answer: X-rays are widely used in medical imaging for internal body scans. So, the correct answer is (a) X-rays.
Q15. The electromagnetic wave is:
(a) Longitudinal
(b) Transverse
(c) Partly longitudinal
(d) Neither longitudinal nor transverse
Answer: EM waves are transverse waves where E and B fields are perpendicular to wave motion. So, the correct answer is (b) Transverse.
Q16. Which of the following has the longest wavelength?
(a) Gamma rays
(b) X-rays
(c) Radio waves
(d) Ultraviolet rays
Answer: Radio waves have the longest wavelength in the electromagnetic spectrum. So, the correct answer is (c) Radio waves.
Q17. The ratio of electric energy density to magnetic energy density in EM waves is:
(a) 1:1
(b) 2:1
(c) 1:2
(d) 4:1
Answer: Electric and magnetic energy densities are always equal in EM waves, so the ratio is 1:1.
Q18. Electromagnetic waves do not require:
(a) Source
(b) Medium
(c) Energy
(d) Time
Answer: EM waves can travel in vacuum, so they do not require any medium. The correct answer is (b) Medium.
Q19. The frequency range of visible light is approximately:
(a) 4×1014–7.5×1014 Hz4 \times 10^{14} – 7.5 \times 10^{14} \, Hz
(b) 3×109–3×1011 Hz3 \times 10^9 – 3 \times 10^{11} \, Hz
(c) >3×1019 Hz> 3 \times 10^{19} \, Hz
(d) <3×109 Hz< 3 \times 10^9 \, Hz
Answer: Visible light has a frequency range of 4×1014–7.5×1014 Hz4 \times 10^{14} – 7.5 \times 10^{14} \, Hz. So, the correct answer is (a).
Q20. The energy flow per unit area in EM waves is given by:
(a) Ampere’s Law
(b) Poynting Vector
(c) Gauss’s Law
(d) Coulomb’s Law
Answer: The energy flow per unit area per unit time is given by the Poynting vector. So, the correct answer is (b) Poynting Vector.
Short Answer Questions
Q1. What are electromagnetic waves?
Answer: Electromagnetic waves are oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation. They do not require any medium for transmission and can travel in a vacuum with the speed of light.
Q2. Name the scientist who gave the theoretical and experimental proof of electromagnetic waves.
Answer: James Clerk Maxwell gave the theoretical proof of electromagnetic waves through his famous Maxwell’s equations in 1864, while Heinrich Hertz provided experimental proof in 1887 by generating and detecting radio waves.
Q3. Define Poynting vector.
Answer: The Poynting vector represents the rate of energy flow per unit area carried by an electromagnetic wave. It is given by S=1μ0(E×B)S = \frac{1}{\mu_0}(E \times B) and its direction is the same as the direction of wave propagation.
Q4. What is the speed of electromagnetic waves in a vacuum?
Answer: The speed of electromagnetic waves in a vacuum is c=3×108 m/sc = 3 \times 10^8 \, m/s. It is a fundamental constant and is independent of the wave’s frequency or wavelength.
Q5. Give two applications of infrared radiation.
Answer: Infrared radiation is used in night vision cameras to detect heat signatures and in TV remote controls for wireless communication between devices.
Long Answer Questions
Q1. Explain Maxwell’s equations and their significance.
Answer: Maxwell’s equations are a set of four fundamental laws that describe how electric and magnetic fields are generated and altered. These include Gauss’s Law for electricity, Gauss’s Law for magnetism, Faraday’s Law of electromagnetic induction, and Ampere-Maxwell’s Law. Collectively, they unify electricity and magnetism into electromagnetism and predict the existence of electromagnetic waves that travel at the speed of light.
Q2. Describe the electromagnetic spectrum in detail.
Answer: The electromagnetic spectrum is the complete range of electromagnetic radiation classified according to wavelength or frequency. It includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Each region has specific properties and applications—for example, radio waves are used in broadcasting, microwaves in satellite communication, infrared in thermal imaging, visible light for vision, ultraviolet for sterilization, X-rays in medical imaging, and gamma rays in nuclear research.
Q3. Discuss the properties of electromagnetic waves.
Answer: Electromagnetic waves are transverse in nature with electric and magnetic fields oscillating perpendicular to each other. They travel with the speed of light in a vacuum, carry energy and momentum, and exhibit wave phenomena like reflection, refraction, diffraction, interference, and polarization. They do not require any medium for propagation, making them different from mechanical waves.
Q4. Explain the concept of polarization in electromagnetic waves.
Answer: Polarization refers to the phenomenon in which the vibrations of the electric field vector in an electromagnetic wave are restricted to one direction. Unpolarized light has vibrations in all directions perpendicular to the direction of wave propagation, while polarized light has vibrations in a single direction. Polarization can be achieved using Polaroid filters, reflection, or scattering methods.
Q5. How is energy distributed in an electromagnetic wave?
Answer: In an electromagnetic wave, the total energy density is equally divided between the electric and magnetic fields. The energy density of the electric field is uE=12ϵ0E2u_E = \frac{1}{2}\epsilon_0 E^2, and that of the magnetic field is uB=12μ0B2u_B = \frac{1}{2\mu_0} B^2. The total energy density is u=uE+uBu = u_E + u_B, and both components contribute equally to the energy carried by the wave.
Frequently Asked Questions (FAQs)
Q1. What are electromagnetic waves made of?
Answer: Electromagnetic waves consist of oscillating electric and magnetic fields. These fields are perpendicular to each other and to the direction of wave propagation, forming a transverse wave.
Q2. Who discovered electromagnetic waves?
Answer: James Clerk Maxwell predicted the existence of electromagnetic waves through his theoretical work in 1864, and Heinrich Hertz experimentally confirmed their existence in 1887.
Q3. What is the speed of electromagnetic waves in vacuum?
Answer: The speed of electromagnetic waves in a vacuum is c=3×108 m/sc = 3 \times 10^8 \, m/s, which is also the speed of light.
Q4. What are some applications of electromagnetic waves?
Answer: Electromagnetic waves have applications in communication (radio, TV, mobile), medical imaging (X-rays), sterilization (ultraviolet rays), thermal imaging (infrared rays), and nuclear research (gamma rays).
Q5. What is the electromagnetic spectrum?
Answer: The electromagnetic spectrum is the range of all possible frequencies and wavelengths of electromagnetic radiation, including radio waves, microwaves, infrared rays, visible light, ultraviolet rays, X-rays, and gamma rays.
Conclusion
Electromagnetic waves form the backbone of modern technology. From simple communication to advanced medical imaging, their applications are vast. A clear understanding of their properties, spectrum, and mathematical representation helps students build strong concepts in physics and score better in exams.