Electromagnetic Waves – Class 12 Physics Chapter 8 Notes & NCERT PDF

Class 12PhysicsChapter 8NCERT book: Physics Part I - Class 12

Notes and a simple summary of Chapter 8 of the NCERT Class 12 Physics book, with the official chapter PDF, flashcards, an MCQ quiz and an AI tutor for your doubts.

🎧 Listen to the content

Chapter 8: Electromagnetic Waves

Introduction

In Chapter 6 you saw that a changing magnetic field produces an electric field. James Clerk Maxwell asked whether the reverse is also true, and found that a changing electric field produces a magnetic field. To make Ampere's circuital law consistent, he added a term called the displacement current. His equations then predicted waves of coupled electric and magnetic fields travelling at 3 × 10⁸ m/s, the speed of light. Light itself turned out to be an electromagnetic wave. Hertz produced such waves in 1887; Jagadish Chandra Bose in Kolkata produced millimetre waves soon after, and Marconi sent radio signals over long distances. Radio, TV, mobile phones, microwave ovens, X-ray machines and remote controls all use parts of the electromagnetic spectrum studied in this chapter.

Key Concepts

8.2 Displacement Current

Apply Ampere's law, ∮B·dl = µ₀i, to a point outside a charging capacitor. With a flat surface cut by the wire, the result is B(2πr) = µ₀i. With a pot-shaped surface passing between the plates, no conduction current crosses it, giving B = 0. This contradiction means Ampere's law is incomplete.

Between the plates, the electric flux is Φ_E = EA = Q/ε₀, so ε₀ dΦ_E/dt = dQ/dt = i. Maxwell called this the displacement current, i_d = ε₀ dΦ_E/dt.

Total current i = i_c + i_d. The Ampere-Maxwell law is ∮B·dl = µ₀i_c + µ₀ε₀ dΦ_E/dt.

Outside the plates only conduction current exists (i_d = 0); inside, only displacement current (i_c = 0, i_d = i). Current is continuous.

Maxwell's equations in vacuum: ∮E·dA = Q/ε₀ (Gauss, electricity); ∮B·dA = 0 (Gauss, magnetism); ∮E·dl = −dΦ_B/dt (Faraday); ∮B·dl = µ₀i_c + µ₀ε₀ dΦ_E/dt (Ampere-Maxwell).

8.3 Electromagnetic Waves

8.3.1 Sources: stationary charges and steady currents do not radiate. Accelerated charges radiate em waves. A charge oscillating with frequency ν produces an em wave of the same frequency ν; the wave's energy comes from the source.

8.3.2 Nature: for a wave travelling along z, E_x = E₀ sin(kz − ωt) and B_y = B₀ sin(kz − ωt).

E and B are perpendicular to each other and to the direction of propagation: em waves are transverse, and propagation is along E × B.

k = 2π/λ, ω = 2πν and ω = ck, so νλ = c.

c = 1/√(µ₀ε₀) = 3 × 10⁸ m/s.

B₀ = E₀/c.

In a medium, v = 1/√(µε), so the speed depends on the medium's electric and magnetic properties.

EM waves need no material medium; they are self-sustaining oscillations of E and B.

They carry energy (sunlight makes life possible) and the speed c is so well known that it is used to define the metre.

8.4 Electromagnetic Spectrum

The spectrum, in order of decreasing wavelength (increasing frequency), with no sharp boundaries:

8.4.1 Radio waves (> 0.1 m): from accelerated charges in wires and aerials. AM band 530–1710 kHz, short wave up to 54 MHz, TV 54–890 MHz, FM 88–108 MHz; mobile phones use the UHF band.

8.4.2 Microwaves (0.1 m to 1 mm, GHz range): from klystrons, magnetrons and Gunn diodes. Used in radar, speed guns and microwave ovens, whose frequency matches the resonant frequency of water molecules.

8.4.3 Infrared (1 mm to 700 nm): from hot bodies and molecular vibrations; "heat waves". Used in physiotherapy lamps, TV remote controls and satellites; responsible for the greenhouse effect.

8.4.4 Visible light (700–400 nm, about 4 × 10¹⁴ to 7 × 10¹⁴ Hz): detected by the eye. Snakes can detect infrared; many insects see into the ultraviolet.

8.4.5 Ultraviolet (400 nm down to 0.6 nm): from the sun and special lamps. Mostly absorbed by the ozone layer at 40–50 km. Causes tanning; absorbed by ordinary glass. Used in LASIK eye surgery and water purifiers. Welders wear protective goggles.

8.4.6 X-rays (about 10 nm down to 10⁻⁴ nm): produced by bombarding a metal target with high-energy electrons. Used in medical diagnosis and cancer treatment.

8.4.7 Gamma rays (below about 10⁻¹⁰ m, down to less than 10⁻¹⁴ m): from nuclear reactions and radioactive decay. Used to destroy cancer cells.

Worked Examples

Example 1 (Book Example 8.1). A 25 MHz plane wave travels along x; at a point E = 6.3 ĵ V/m. B = E/c = 6.3/(3 × 10⁸) = 2.1 × 10⁻⁸ T. Since E × B must point along +x and ĵ × k̂ = î, B = 2.1 × 10⁻⁸ k̂ T.

Example 2 (Book Example 8.2). B_y = 2 × 10⁻⁷ sin(0.5 × 10³x + 1.5 × 10¹¹t) T. λ = 2π/k = 2π/500 ≈ 1.26 cm; ν = ω/2π = 1.5 × 10¹¹/2π ≈ 23.9 GHz; E₀ = B₀c = 60 V/m, so E_z = 60 sin(0.5 × 10³x + 1.5 × 10¹¹t) V/m.

Example 3 (Exercise 8.1). Circular plates of radius 12 cm, 5.0 cm apart, charging current 0.15 A. C = ε₀πr²/d ≈ 8.0 pF; dV/dt = I/C ≈ 1.87 × 10¹⁰ V/s; displacement current = 0.15 A. Kirchhoff's junction rule holds at each plate if the displacement current is included.

Example 4 (Exercises 8.4 and 8.5). A 30 MHz wave: λ = c/ν = 10 m. A radio tuning 7.5–12 MHz covers wavelengths 40 m to 25 m.

Example 5 (Exercise 8.10). ν = 2.0 × 10¹⁰ Hz, E₀ = 48 V/m: λ = 1.5 cm, B₀ = E₀/c = 1.6 × 10⁻⁷ T. The average energy densities of the E and B fields are equal.

Formula and Key-Facts Sheet

Displacement current: i_d = ε₀ dΦ_E/dt

Ampere-Maxwell law: ∮B·dl = µ₀i_c + µ₀ε₀ dΦ_E/dt

c = 1/√(µ₀ε₀) = 3 × 10⁸ m/s; in a medium v = 1/√(µε)

νλ = c; ω = ck; k = 2π/λ

B₀ = E₀/c; propagation along E × B

Order: radio > microwave > infrared > visible > UV > X-rays > gamma (wavelength)

Visible: 400–700 nm; FM 88–108 MHz; AM 530–1710 kHz

Ozone absorbs most UV at 40–50 km altitude

Board Exam Focus

Common questions: need for displacement current and its expression; Ampere-Maxwell law; properties of em waves; B₀ = E₀/c problems; identifying a part of the spectrum from its use or wavelength, and its source; arranging the spectrum in order.

Answer outline: "Why did Maxwell introduce displacement current?" Ampere's law applied to two surfaces bounded by the same loop near a charging capacitor gives different B (µ₀i/2πr and zero). Maxwell added i_d = ε₀ dΦ_E/dt, which equals the conduction current i between the plates, making current continuous and the law consistent.

Answer outline: Exercise 8.8. E₀ = 120 N/C, ν = 50.0 MHz. B₀ = E₀/c = 400 nT; ω = 2πν ≈ 3.14 × 10⁸ rad/s; k = ω/c ≈ 1.05 rad/m; λ = c/ν = 6.0 m. E = 120 sin(1.05x − 3.14 × 10⁸t) ĵ N/C and B = 400 sin(1.05x − 3.14 × 10⁸t) k̂ nT.

Answer outline: "Name the em waves used for (i) radar, (ii) TV remote, (iii) killing germs in water, (iv) bone fracture diagnosis." Microwaves; infrared; ultraviolet; X-rays. Add one line on how each is produced.

Key Terms

Displacement current (विस्थापन धारा)

Conduction current (चालन धारा)

Electric flux (विद्युत फ्लक्स)

Electromagnetic wave (विद्युत चुंबकीय तरंग)

Transverse wave (अनुप्रस्थ तरंग)

Electromagnetic spectrum (विद्युत चुंबकीय स्पेक्ट्रम)

Radio waves (रेडियो तरंगें)

Microwaves (सूक्ष्म तरंगें)

Infrared rays (अवरक्त किरणें)

Ultraviolet rays (पराबैंगनी किरणें)

X-rays (एक्स-किरणें)

Gamma rays (गामा किरणें)

Ozone layer (ओज़ोन परत)

Greenhouse effect (ग्रीनहाउस प्रभाव)

Common Mistakes

Thinking displacement current is a flow of charges. It is a changing electric flux that produces a magnetic field just like a current.

Writing E₀ = B₀/c instead of B₀ = E₀/c (B is much smaller numerically).

Getting the direction of B wrong. Propagation is along E × B, so use the cross product.

Assuming the frequency of the em wave differs from the frequency of the oscillating charge. They are equal.

Swapping the order of UV and X-rays, or of infrared and microwaves, in the spectrum.

Saying em waves need a medium; they travel through vacuum at c.

Using ω in place of ν in νλ = c.

💡 Key Learning Points

✓Maxwell's displacement current i_d = ε₀ dΦ_E/dt removes the inconsistency in Ampere's law and gives the Ampere-Maxwell law.
✓Accelerated charges radiate em waves whose frequency equals the frequency of the oscillating charge.
✓EM waves are transverse: E, B and the direction of propagation are mutually perpendicular, with B₀ = E₀/c and propagation along E × B.
✓In vacuum em waves travel at c = 1/√(µ₀ε₀) = 3 × 10⁸ m/s, need no medium and carry energy; in a medium v = 1/√(µε).
✓The spectrum from long to short wavelength is radio, microwave, infrared, visible, ultraviolet, X-rays and gamma rays, each with its own sources and uses.

👨‍🏫 Teaching Tips

→Draw the two surfaces (flat and pot-shaped) for Ampere's law near a capacitor to make the contradiction obvious.
→Use a 3D sketch or a hand model (three fingers) to show E, B and the direction of travel at right angles.
→Have students calculate 1/√(µ₀ε₀) themselves to discover that it equals the speed of light.
→Make a class spectrum wall chart with wavelength, source, detector and daily-life use for each band.
→Use a phone camera to see the infrared LED of a TV remote flashing.
→Mention J. C. Bose's millimetre-wave work to connect the chapter to Indian science history.
→Practise quick λ = c/ν conversions using FM, AM and mobile frequencies students already know.

📋 Assessment Questions

Explain the need for displacement current and write the Ampere-Maxwell law.
State the properties of em waves and use B₀ = E₀/c, c = νλ and c = 1/√(µ₀ε₀).
Find the direction of B (or E) from the direction of propagation using E × B.
Arrange em waves in order of wavelength or frequency and give the source and one use of each.
Solve numericals on capacitor displacement current and wave parameters (λ, ν, k, ω, E₀, B₀).

Ask the AI tutor about Class 12 Physics Chapter 8

Get question answers, important questions, a quick MCQ quiz or a simple explanation of “Electromagnetic Waves”. Free — sign in with Google.

How the AI tutor works →

👩‍🏫 Class 12 Physics classes near you — online or at home

Prefer a real teacher? TalentJR teachers take live online classes anywhere in India and visit homes in selected cities. Tell us what you need and our team will call you with timings and fees.

Live online classesSmall groups or 1:1 with a teacher, from home, any city.
Teacher at homeA TalentJR teacher visits your home (selected cities).
At a centreClasses at a TalentJR partner centre near you, where available.

Keep learning

← Previous: Chapter 7Alternating Current