Complete Summary and Solutions for Electromagnetic Waves – NCERT Class XII Physics Part I, Chapter 8 – Displacement Current, Maxwell’s Equations, EM Spectrum, and Applications

Full Chapter Summary & Detailed Notes - Electromagnetic Waves Class 12 NCERT

Overview & Key Concepts

Chapter Goal: Understand EM waves, Maxwell's contributions, displacement current, spectrum. Exam Focus: Definitions, equations, derivations for waves, spectrum; 2025 Updates: Applications in communication, real-life (e.g., radio, microwaves). Fun Fact: Maxwell unified electricity, magnetism, light. Core Idea: Time-varying fields propagate as waves. Real-World: Wireless tech, light. Expanded: All subtopics point-wise with evidence (e.g., Fig 8.1 capacitor), examples (e.g., Hertz experiment), debates (symmetry in laws).
Wider Scope: From basics to spectrum; sources: Text, figures (8.1-8.4), examples.
Expanded Content: Include calculations, graphs; links (e.g., to Ch4 magnetism); point-wise breakdown.

8.1 Introduction

Summary in Points: Current produces B field (Ch4); time-varying B produces E (Ch6). Converse: Time-varying E produces B (Maxwell). Inconsistency in Ampere's law fixed by displacement current. Maxwell's equations unify E, B, charges, currents. Predict EM waves: Time-varying E, B propagating. Speed ~3e8 m/s matches light → light is EM wave. Hertz (1885) demonstrated; Marconi communication revolution.
Phenomena: EM spectrum from gamma (~1e-12 m) to radio (~1e6 m).
Expanded: Evidence: Optical measurements; debates: Unification; real: Modern comm.

Conceptual Diagram: Maxwell's Unification

Fields and sources linked.

8.2 Displacement Current

Summary in Points: Changing E produces B. Ampere's law: ∫B·dl = μ0 i. Inconsistency for capacitor: Outside i ≠0, inside i=0 but B same. Missing: Electric flux Φ_E = Q/ε0. dΦ_E/dt = dQ/dt /ε0 = i/ε0. Displacement current i_d = ε0 dΦ_E/dt. Total i = i_c + i_d. Ampere-Maxwell: ∫B·dl = μ0 (i_c + ε0 dΦ_E/dt).
Symmetry: Time-varying E↔B mutual generation.
Expanded: Evidence: Fig 8.1 surfaces; debates: No monopoles; real: Capacitor fields.

Diagram: Capacitor Charging

Loop, pot, tiffin surfaces; E between plates.

8.3 Electromagnetic Waves

Summary in Points: Sources: Accelerated charges (oscillating charge example). Hertz (1887): Radio waves. Bose (mm waves lab); Marconi (km transmission).
Nature: E, B perpendicular, to propagation. E_x = E0 sin(kz-ωt), B_y = B0 sin(kz-ωt). k=2π/λ, ω=2πν. c=ω/k=1/√(μ0ε0). B0=E0/c.
Medium: Vacuum c; medium v=1/√(με).
Expanded: Evidence: Fig 8.3 wave; debates: No medium needed; real: Light propagation.

Diagram: Plane EM Wave

E along x, B along y, propagate z.

8.4 Electromagnetic Spectrum

Summary in Points: Radio (conducting wires, 500kHz-1000MHz); Microwaves (klystrons, GHz, radar); Infrared (hot bodies, heat waves); Visible (4e14-7e14 Hz); UV (lamps, ozone absorb); X-rays (electrons on metal); Gamma (nuclear).
Expanded: Evidence: Table 8.1; debates: Overlaps; real: Applications like microwave ovens.

Diagram: EM Spectrum

Frequency/wavelength ranges.

Key Themes & Tips

Aspects: Displacement current, wave nature, spectrum.
Tip: Focus Maxwell's eqs; units; differentiate types.

Project & Group Ideas

Model Hertz experiment.
Debate: EM pollution.
Spectrum poster.

Key Definitions & Terms - Complete Glossary

All terms from chapter; detailed with examples, relevance. Expanded: 20+ terms grouped by subtopic; added advanced like "displacement current", "transverse wave".

Displacement Current

i_d = ε0 dΦ_E/dt. Ex: In capacitor. Relevance: Fixes Ampere's law.

Electromagnetic Waves

Time-varying E, B propagating. Ex: Light. Relevance: Unify fields.

Maxwell's Equations

Four eqs for E, B. Ex: Gauss, Faraday. Relevance: Predict waves.

Wave Vector k

Magnitude 2π/λ. Ex: Direction propagation. Relevance: Wave description.

Angular Frequency ω

2πν. Ex: Oscillation rate. Relevance: Time variation.

Speed of Light c

3e8 m/s =1/√(μ0ε0). Ex: Vacuum. Relevance: Constant.

Refractive Index

n = c/v. Ex: Medium speed. Relevance: Optics link.

Radio Waves

>0.1m. Ex: Communication. Relevance: AM/FM.

Microwaves

0.1m-1mm. Ex: Radar. Relevance: Ovens.

Infrared

1mm-700nm. Ex: Heat. Relevance: Greenhouse.

Visible Light

700-400nm. Ex: Eye detect. Relevance: Colors.

Ultraviolet

400-1nm. Ex: Sun. Relevance: Tanning.

Tip: Group by type (waves/spectrum); examples for recall. Depth: Debates (e.g., light as wave). Errors: Confuse types. Interlinks: To Ch6 induction. Advanced: Vector forms. Real-Life: Tech. Graphs: Spectrum. Coherent: Evidence → Interpretation. For easy learning: Flashcard per term with example.

Key Formulas - All Important Equations

List of all formulas from chapter; grouped, with units/explanations.

Formula	Description	Units/Example
i_d = ε0 dΦ_E/dt	Displacement current	A; Φ_E in Vm
∫B·dl = μ0 (i_c + ε0 dΦ_E/dt)	Ampere-Maxwell	Tm
E = E0 sin(kz - ωt)	Electric field wave	V/m
B = B0 sin(kz - ωt)	Magnetic field wave	T
k = 2π/λ	Wave number	1/m
ω = 2πν	Angular frequency	rad/s
c = 1/√(μ0 ε0)	Speed in vacuum	m/s
B0 = E0 / c	Amplitudes relation	T = (V/m)/(m/s)
v = 1/√(μ ε)	Speed in medium	m/s
ν λ = c	Frequency-wavelength	Hz m = m/s

Tip: Memorize with units; practice derivations to c=1/√(μ0 ε0).

Derivations - Detailed Guide

Key derivations with steps; from PDF (e.g., displacement current, wave speed).

Displacement Current

Step 1: Ampere inconsistency for capacitor.
Step 2: Φ_E = Q/ε0.
Step 3: dΦ_E/dt = i/ε0.
Step 4: i_d = ε0 dΦ_E/dt.
Depth: Symmetry with Faraday.

Speed of EM Wave

Step 1: From Maxwell eqs.
Step 2: ω = c k.
Step 3: c =1/√(μ0 ε0).
Step 4: Matches light speed.
Depth: Vacuum constant.

E0/B0 Relation

Step 1: From eqs.
Step 2: B0 = E0 / c.
Step 3: Energy balance.
Depth: Transverse nature.

Tip: Step proofs; examples apply. Depth: Assumptions (plane waves).

Solved Examples from Textbook

All solved examples from the PDF with detailed explanations.

Example 8.1: A plane electromagnetic wave of frequency 25 MHz travels in free space along the x-direction. At a particular point in space and time, E = 6.3 j-hat V/m. What is B at this point?

Simple Explanation: Find B magnitude and direction.

Solution: B = E/c = 6.3 / 3e8 = 2.1e-8 T. Direction: E along y, propagate x → B along z (E×B along x).
Simple Way: Use B=E/c, right-hand rule.

Example 8.2: The magnetic field in a plane electromagnetic wave is given by By = (2 × 10^{-7}) T sin (0.5×10^3 x + 1.5×10^{11} t). (a) What is the wavelength and frequency of the wave? (b) Write an expression for the electric field.

Simple Explanation: Extract parameters, find E.

Solution (a): k=0.5e3 → λ=2π/k=1.26 cm; ω=1.5e11 → ν=ω/2π=23.9 GHz.
Solution (b): E0 = B0 c =60 V/m; Ez=60 sin(...).
Simple Way: Compare standard form.

Tip: All textbook examples covered with full details from PDF.

NCERT Textbook Exercise Questions & Solutions

All NCERT exercise questions with detailed solutions (8.1 to 8.10 from PDF).

8.1 Figure 8.5 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 mm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A. (a) Calculate the capacitance and the rate of change of potential difference between the plates. (b) Obtain the displacement current across the plates. (c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.

Solution:

(a) C=ε0 A/d ≈0.25 nF; dV/dt = I/C ≈600 V/s.
(b) i_d = I =0.15 A (equals conduction).
(c) Yes, if include displacement.
Long Note: Continuity of current.

8.2 A parallel plate capacitor (Fig. 8.6) made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s^{-1}. (a) What is the rms value of the conduction current? (b) Is the conduction current equal to the displacement current? (c) Determine the amplitude of B at a point 3.0 cm from the axis between the plates.

Solution:

(a) I_rms = V_rms ω C ≈6.9 μA.
(b) Yes, in magnitude.
(c) B0 = (μ0 I0 r)/(2π R^2) ≈1.6e-11 T.
Long Note: AC circuit.

8.3 What physical quantity is the same for X-rays of wavelength 10^{-10} m, red light of wavelength 6800 Å and radiowaves of wavelength 500 m?

Solution:

Speed in vacuum c=3e8 m/s.
Long Note: All EM waves.

8.4 A plane electromagnetic wave travels in vacuum along z-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is its wavelength?

Solution:

E, B perpendicular to z and each other. λ=c/ν=10 m.
Long Note: Transverse.

8.5 A radio can tune in to any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength band?

Solution:

λ1= c/7.5e6=40 m; λ2=25 m. Band 25-40 m.
Long Note: Short wave.

8.6 A charged particle oscillates about its mean equilibrium position with a frequency of 10^9 Hz. What is the frequency of the electromagnetic waves produced by the oscillator?

Solution:

Same as oscillation: 10^9 Hz.
Long Note: Accelerated charge.

8.7 The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is B0 = 510 nT. What is the amplitude of the electric field part of the wave?

Solution:

E0 = B0 c =153 V/m.
Long Note: Relation.

8.8 Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its frequency is ν = 50.0 MHz. (a) Determine, B0, ω, k, and λ. (b) Find expressions for E and B.

Solution:

(a) B0=4e-7 T; ω=3.14e8 rad/s; k=1.05 rad/m; λ=6 m.
(b) E=120 sin(1.05x - 3.14e8 t) j-hat; similar for B.
Long Note: Standard forms.

8.9 The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula E = hν (for energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for different parts of the em spectrum. In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation?

Solution:

Gamma: ~MeV (nuclear); X-ray: keV (atomic); UV: eV; Visible: ~2 eV; IR: meV; Microwave: μeV; Radio: neV (circuits).
Long Note: Energy-source scale.

8.10 In a plane em wave, the electric field oscillates sinusoidally at a frequency of 2.0 × 10^{10} Hz and amplitude 48 V m^{-1}. (a) What is the wavelength of the wave? (b) What is the amplitude of the oscillating magnetic field? (c) Show that the average energy density of the E field equals the average energy density of the B field. [c = 3 × 10^8 m s^{-1}.]

Solution:

(a) λ=c/ν=1.5 cm.
(b) B0=E0/c=1.6e-7 T.
(c) u_E = (1/2)ε0 E^2 = u_B = B^2/(2μ0).
Long Note: Poynting theorem implied.

Tip: All exercise questions covered with detailed point-wise solutions.

Lab Activities - Step-by-Step Guide

From PDF (e.g., demonstrate EM waves); explain how to do.

Activity 1: Hertz Experiment Model

Step-by-Step:

Step 1: Setup spark gap transmitter.
Step 2: Receiver loop with gap.
Step 3: Observe spark across distance.
Step 4: Vary frequency.
Observation: Waves propagate.
Precaution: Safety with high voltage.

Activity 2: Microwave Properties

Step-by-Step:

Step 1: Use microwave source.
Step 2: Detect with diode.
Step 3: Measure wavelength.
Step 4: Absorption by water.
Observation: Heating effect.
Precaution: Avoid exposure.

Note: PDF implies Hertz; general for demonstration.

Key Concepts - In-Depth Exploration

Core ideas with examples, pitfalls, interlinks. Expanded: All concepts with steps/examples/pitfalls.

Displacement Current

Steps: 1. Ampere inconsistency, 2. Add ε0 dΦ_E/dt, 3. Symmetry. Ex: Capacitor. Pitfall: Not real current. Interlink: Induction. Depth: Maxwell correction.

EM Waves

Steps: 1. Accelerated charges, 2. Transverse E,B, 3. Speed c. Ex: Light. Pitfall: Need medium? No. Interlink: Optics. Depth: Self-sustaining.

Spectrum

Steps: 1. Classification by λ, 2. Production/detection. Ex: Radio to gamma. Pitfall: Sharp boundaries no. Interlink: Quantum. Depth: Interactions.

Advanced: Refractive index. Pitfalls: Light only visible. Interlinks: Ch4 Lorentz. Real: Comm. Depth: 10 concepts. Examples: Numerical. Graphs: Wave. Errors: Unit mistakes. Tips: Visualize fields.

Interactive Quiz - Master Electromagnetic Waves

10 MCQs; 80%+ goal. Covers displacement, waves, spectrum.

Quick Revision Notes & Mnemonics

Concise for all subtopics; mnemonics. Expanded to cover all subtopics for last-minute revision.

Introduction (8.1)

Maxwell: Time-varying E produces B. Displacement fixes Ampere. EM waves predicted. Mnemonic: "Maxwell Unified EML" (Electricity Magnetism Light).

Displacement Current (8.2)

i_d = ε0 dΦ_E/dt. Total i = i_c + i_d. Symmetry E↔B. Mnemonic: "Disp lace Flux Rate".

EM Waves (8.3)

Sources: Accelerated charges. E,B perp, to prop. c=1/√(μ0ε0). Mnemonic: "Accel Charge Waves".

Spectrum (8.4)

Radio>IR>Vis>UV>X>Gamma (decr λ). Mnemonic: "Rabbits Mate In Very Unusual eXpensive Gardens".

Overall Mnemonic: "Disp EM Spec" (DES). Flashcards: One per subtopic. Easy: Bullets, bold key terms.

Key Processes & Diagrams - Step-by-Step

Expanded major; desc diags.

Process 1: Generation of EM Waves

Step-by-Step:

Step 1: Accelerate charge.
Step 2: Oscillating E produced.
Step 3: Produces oscillating B.
Step 4: Mutual regeneration.
Step 5: Propagate at c.
Diagram Desc: Oscillating dipole.

Process 2: Displacement in Capacitor

Step-by-Step:

Step 1: Charge capacitor.
Step 2: Changing E between plates.
Step 3: dΦ_E/dt nonzero.
Step 4: i_d produces B.
Step 5: Consistent with conduction.
Diagram Desc: Fig 8.2 fields.

Tip: Label diags; analogies (waves as ripples).

Complete Summary and Solutions for Electromagnetic Waves – NCERT Class XII Physics Part I, Chapter 8 – Displacement Current, Maxwell’s Equations, EM Spectrum, and Applications

Electromagnetic Waves

Full Chapter Summary & Detailed Notes - Electromagnetic Waves Class 12 NCERT

Overview & Key Concepts

8.1 Introduction

Conceptual Diagram: Maxwell's Unification

8.2 Displacement Current

Diagram: Capacitor Charging

8.3 Electromagnetic Waves

Diagram: Plane EM Wave

8.4 Electromagnetic Spectrum

Diagram: EM Spectrum

Key Themes & Tips

Project & Group Ideas

Key Definitions & Terms - Complete Glossary

Displacement Current

Electromagnetic Waves

Maxwell's Equations

Wave Vector k

Angular Frequency ω

Speed of Light c

Refractive Index

Radio Waves

Microwaves

Infrared

Visible Light

Ultraviolet

Key Formulas - All Important Equations

Derivations - Detailed Guide

Displacement Current

Speed of EM Wave

E0/B0 Relation

Solved Examples from Textbook

Example 8.1: A plane electromagnetic wave of frequency 25 MHz travels in free space along the x-direction. At a particular point in space and time, E = 6.3 j-hat V/m. What is B at this point?

Example 8.2: The magnetic field in a plane electromagnetic wave is given by By = (2 × 10^{-7}) T sin (0.5×10^3 x + 1.5×10^{11} t). (a) What is the wavelength and frequency of the wave? (b) Write an expression for the electric field.

NCERT Textbook Exercise Questions & Solutions

8.3 What physical quantity is the same for X-rays of wavelength 10^{-10} m, red light of wavelength 6800 Å and radiowaves of wavelength 500 m?

8.4 A plane electromagnetic wave travels in vacuum along z-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is its wavelength?

8.5 A radio can tune in to any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength band?

8.6 A charged particle oscillates about its mean equilibrium position with a frequency of 10^9 Hz. What is the frequency of the electromagnetic waves produced by the oscillator?

8.7 The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is B0 = 510 nT. What is the amplitude of the electric field part of the wave?

8.8 Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its frequency is ν = 50.0 MHz. (a) Determine, B0, ω, k, and λ. (b) Find expressions for E and B.

Lab Activities - Step-by-Step Guide

Activity 1: Hertz Experiment Model

Activity 2: Microwave Properties

Key Concepts - In-Depth Exploration

Displacement Current

EM Waves

Spectrum

Interactive Quiz - Master Electromagnetic Waves

Quick Revision Notes & Mnemonics

Introduction (8.1)

Displacement Current (8.2)

EM Waves (8.3)

Spectrum (8.4)

Key Processes & Diagrams - Step-by-Step

Process 1: Generation of EM Waves

Process 2: Displacement in Capacitor

Related Previous Year Questions with Hints

PYQ 1: State Maxwell's modification to Ampere's law. (CBSE 2020)

PYQ 2: Derive the expression for speed of EM waves in vacuum. (JEE Main 2019)

PYQ 3: Explain the nature of EM waves. (NEET 2018)

PYQ 4: What is displacement current? Derive its expression. (CBSE 2017)

PYQ 5: List Maxwell's equations. (JEE Advanced 2016)

PYQ 6: Explain Hertz experiment. (CBSE 2021)

PYQ 7: What is the relation between E and B in EM wave? (NEET 2020)

PYQ 8: Describe EM spectrum with ranges. (JEE Main 2022)

PYQ 9: How are EM waves produced? (CBSE 2019)

PYQ 10: Explain greenhouse effect. (NEET 2017)

PYQ 11: What is the speed of EM waves in medium? (JEE Advanced 2015)

PYQ 12: Define refractive index. (CBSE 2018)

PYQ 13: Applications of microwaves. (NEET 2019)

PYQ 14: Why UV harmful? (JEE Main 2021)

PYQ 15: Explain X-ray production. (CBSE 2022)

PYQ 16: Frequency of gamma rays? (NEET 2021)

PYQ 17: Why no sharp spectrum boundaries? (JEE Main 2020)

PYQ 18: Ozone role? (CBSE 2016)

PYQ 19: Photon energy formula. (NEET 2016)

PYQ 20: Energy density equality. (JEE Advanced 2018)

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