Chapter 15 · Class 11-12 & JEE/NEET

Magnetic Effects of Current & Magnetism

68 topics in 16 parts

Full lessonClass 12 Physics · Moving Charges and Magnetism Practice276 practice questions

Lorentz Force Magnetic Force on a Moving Charge Charged Particle Radius in a Magnetic Field Cyclotron Frequency Cyclotron Period Velocity Selector

Key ideas

Rigid Body Rolling Down an Inclined Plane: Dynamics & Friction Direction

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 68 topics in Magnetic Effects of Current & Magnetism

Force on a Moving Charge in Magnetic Field
- Magnetic Force
- Lorentz Force
- Direction & Right-Hand Rules
Charged Particle Motion in Electric & Magnetic Fields
- Circular Motion
- Helical Motion
- Motion in Combined Electric & Magnetic Fields
- Finite Magnetic Field Regions
Applications Involving Charged Particles Moving in a Magnetic Field
- Velocity Selector
- Cyclotron
- Mass Spectrometer
Force on a Current-Carrying Wire
- Direction of Force
- Force & Equilibrium
- Current-Loop Dynamics
Force Between Two Infinite Parallel Current-Carrying Wires
- Parallel Currents & Force
- Equilibrium of Parallel Wires
- Magnetic Pressure
Magnetic Dipole & Dipole Moment
- Current Loop as a Magnetic Dipole
- Magnetic Moment
- Rotating Charges & Charged Bodies
- Orbital Magnetic Moment
Torque on a Current-Carrying Planar Loop in a Uniform Magnetic Field
- Torque in a Uniform Magnetic Field
- Potential Energy of a Magnetic Dipole
- Angular Motion of a Current Loop
Moving Coil Galvanometer
- Construction & Theory
- Current Sensitivity
- Voltage Sensitivity
- Conditions for Sensitivity
- Conversion to Ammeter & Voltmeter
Biot-Savart's Law & Applications
- Moving Point Charge
- Current Element
- Long Straight Wire
- Circular Arc
- Circular Current Loop
- Field on the Axis of a Circular Loop
- Complex Wire Geometries
- Superposition of Magnetic Fields
Ampere's Law & Applications
- Ampere's Circuital Law
- Long Straight Conductor
- Solid Cylindrical Conductor
- Coaxial Cylinders
- Infinite Current Sheet
- Solenoid
- Toroid
Bar Magnet & Gauss's Law for Magnetism
- Bar Magnet as an Equivalent Solenoid
- Pole Strength
- Magnetic Dipole Field
- Axial & Equatorial Fields
- Magnetic Field Lines
- Gauss's Law for Magnetism
Earth's Magnetism
- Elements of Earth's Magnetic Field
- Magnetic Declination & Dip
- Tangent Galvanometer
- Vibration Magnetometer
Magnetisation & Magnetic Intensity
- Magnetisation
- Magnetic Intensity
- Magnetic Susceptibility
- Magnetic Permeability
- Curie Law
Magnetic Properties of Materials
- Diamagnetism
- Paramagnetism
- Ferromagnetism
- Curie Temperature
- Hysteresis Loop
- Magnetic Shielding
Permanent Magnets & Electromagnets
- Permanent Magnets
- Electromagnets
Magnetic Flux & Energy
- Magnetic Flux
- Energy Stored in a Magnetic Field