Chapter 10 · Class 11-12 & JEE/NEET
Electrostatics
53 topics in 11 parts
Coulomb's law Gauss's law Coulomb's Law Superposition of Electric Forces Electric Field Field of a Point Charge
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 53 topics in Electrostatics
Electric Charge & Charging Methods
- Properties of Charge
- Quantization & Conservation of Charge
- Charging by Conduction
- Charging by Friction
- Charging by Induction
- Conductors & Insulators
- Electroscope
Coulomb's Law & Electrostatic Force
- Vector Form
- Superposition Principle
- Equilibrium of Charges
- Comparison with Gravitational Force
- Force Between Point & Continuous Charges
Electric Field & Field Intensity
- Point Charge Field & Vector Notation
- Field of Ring Charge
- Field of Line Charge & Rod
- Field of Charged Disk
- Field of Charged Sheets & Metallic Plates
- Motion of Charged Particles
- Group of Charges & Graphical Variations
Electric Field Lines
- Field Line Properties
- Field Line Patterns
Electric Dipole & Dipole Dynamics
- Axial & Equatorial Field
- Field at General Point
- Torque in Electric Field
- Work Done & Rotation of Dipole
- Dipole in Non-Uniform Field
- Potential & Energy of Dipole
Electric Flux & Gauss's Law
- Flux Calculation & Definition
- Statement & Proof of Gauss's Law
- Selection of Gaussian Surface
- Field of Conducting & Non-conducting Spheres
- Field of Cylinders & Planar Surfaces
- Flux Through Closed Surfaces & Hemispheres
Electric Potential & Potential Difference
- Potential Due to Point Charge & Collection of Charges
- Potential Due to Continuous Charge Distributions
- Potential of Spherical Shells & Solid Spheres
- Relation Between Electric Field & Potential
Equipotential Surfaces & Electrostatic Potential Energy
- Equipotential Surface Properties
- Potential Energy of System of Charges
- Potential Energy in External Field
- Conservation of Electrostatic Energy
Conductors, Induced Charges & Earthing
- Properties of Conductors in Electrostatics
- Electrostatic Shielding & Screening
- Earthing & Grounding of Conductors
- Field & Force on Conducting Surface
- Induced Charges & Cavities in Conductors
Electrostatic Self Energy & Interaction Energy
- Self-Energy of Uniformly Charged Sphere & Shell
- Self & Interaction Energy of Concentric Spheres
- Energy Density of Electric Field
Capacitance & Conductors (Electrostatic Fundamentals)
- Capacitance of Isolated Spheres & Conductors
- Parallel Plate Capacitors & Dielectrics
- Combination of Capacitors
- Energy Stored in Capacitors