Chapter 9 · Class 11-12 & JEE/NEET
Electromagnetic Waves
41 topics in 8 parts
Wave Speed Speed of Light in Vacuum Speed in a Medium Refractive Index Electric–Magnetic Field Ratio Vacuum Field Ratio
Key ideas
4. Systematic Comparison & Parameter Classifications
| Body Shape | Axis of Rotation | Moment of Inertia (I) | Shape Factor (k² / R²) |
|---|---|---|---|
| Thin Ring / Hollow Cylinder | Central Axis Perpendicular to Plane | M R² | 1.0 (Slowest Down Incline) |
| Solid Disc / Solid Cylinder | Central Axis Perpendicular to Plane | (1/2) M R² | 0.50 |
| Solid Sphere | Diameter Axis | (2/5) M R² | 0.40 (Fastest Down Incline) |
| Spherical Shell (Hollow) | Diameter Axis | (2/3) M R² | 0.67 |
| Uniform Rod (Length L) | Through Center Perpendicular to Length | (1/12) M L² | L² / (12 R²) |
Exam Worked Example
Problem: A solid sphere and a solid cylinder of equal mass M and radius R roll down the same inclined plane without slipping from rest. Find the ratio of their accelerations down the incline.
● Step 1: Formula for linear acceleration in pure rolling: a = (g sin θ) / (1 + k²/R²).
● Step 2: For solid sphere, k²/R² = 2/5 = 0.4. Therefore, a_sphere = (g sin θ) / (1 + 2/5) = 5/7 g sin θ ≈ 0.714 g sin θ.
● Step 3: For solid cylinder, k²/R² = 1/2 = 0.5. Therefore, a_cyl = (g sin θ) / (1 + 1/2) = 2/3 g sin θ ≈ 0.667 g sin θ.
● Step 4: Ratio a_sphere / a_cyl = (5/7) / (2/3) = (5 * 3) / (7 * 2) = 15 / 14 ≈ 1.07. The solid sphere reaches the bottom first!
Checkpoint
1. When a ballet dancer pulls her arms inward during a spin on smooth ice, what happens to her kinetic energy?
All 41 topics in Electromagnetic Waves
Displacement Current
- Maxwell's Correction to Ampère's Law
- In Capacitors
Electromagnetic Waves
- Nature of Electromagnetic Waves
- Sources of Electromagnetic Waves
- E-B Field Relationship
- Speed in Vacuum & Media
- Wave Equation & Propagation Direction
- Wavelength & Frequency Relation
- Superposition & Standing Waves
- Force on Charges
- Maxwell's Equations
Energy & Momentum of Electromagnetic Waves
- Energy Density
- Intensity & Energy Flux
- Poynting Vector
- Radiation Pressure & Momentum Transfer
- Inverse-Square Variation of Intensity
Electromagnetic Spectrum
- Spectrum Classification
- Radio Waves
- Microwaves
- Infrared Waves
- Visible Light
- Ultraviolet Rays
- X-Rays
- Gamma Rays
- Frequency Bands & Applications
Electromagnetic Waves Propagation
- Modes of Radio-Wave Propagation
- Ground Wave Propagation
- Sky Wave Propagation
- Space Wave & Line-of-Sight Propagation
- Ionosphere
Amplitude & Frequency Modulation
- Principles of Modulation
- Amplitude Modulation
- Frequency Modulation
- Modulation Index
Bandwidth of Signals & Transmission Medium
- Signal Bandwidth
- Transmission Medium Bandwidth
- Channel Capacity
Basic Elements of a Communication System
- Communication-System Block Diagram
- Transmitter
- Receiver
- Antennas