Chapter 8 · Class 11-12 & JEE/NEET
Electromagnetic Induction
46 topics in 15 parts
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 46 topics in Electromagnetic Induction
Magnetic Flux & EMI
- Calculation of Magnetic Flux
- Flux Linkage & Change in Magnetic Flux
Faraday's Law of Electromagnetic Induction
- Magnitude of Induced EMF
- Direction of Induced EMF
- Induced Current & Charge Flow
Lenz's Law
- Direction of Induced Current in a Circuit
- Opposition to Magnetic Flux Change
- Conservation of Energy in EMI
Motional EMF
- Translational EMF in a Uniform Field
- EMF in a Non-Uniform Magnetic Field
- Rotational EMF in Conducting Rods & Discs
- Circuit Problems with Mechanics & Sliding Rods
Induced Electric Field
- Non-Conservative Electric Field
- Induced EMF in a Stationary Conductor
- Time-Varying Magnetic Field
- Cylindrical & Ring Geometries
Eddy Currents
- Production & Properties
- Electromagnetic Damping & Applications
Self-Inductance
- Inductance of Solenoids & Coils
- Self-Induced EMF
- Factors Affecting Self-Inductance
- Back EMF in Motors
Mutual Inductance
- Coaxial Solenoids & Concentric Loops
- Coefficient of Coupling
- Mutual Induced EMF
- Energy in Coupled Inductors
Series & Parallel Combination of Inductors
- Equivalent Inductance in Series & Parallel
- Inductors with Mutual Coupling
L-R Circuit
- Growth & Decay of Current
- Transient State & Time Constant
- Initial State & Steady State Analysis
- Application of Kirchhoff's Law
Energy Stored in the Magnetic Field of Inductors
- Magnetic Energy Stored in an Inductor
- Magnetic Energy Density
- Energy Dissipation in Resistors
LC Oscillations
- Circuit Analysis
- Frequency & Period
- Energy Exchange Between Electric & Magnetic Fields
RLC Circuits & Resonance
- Damped & Forced Oscillations
- Series Resonance & Q-Factor
- Transient Response
AC Generators
- Principle & Working
- Peak & RMS Induced EMF
Transformers
- Step-Up & Step-Down Transformers
- Turns Ratio & Voltage-Current Relations
- Transformer Losses & Efficiency