Topics
Electrostatics
Electric Charges and Fields
- Electric Charges
- Conductors and Insulators
- Properties of Electric Charge
- Coulomb’s Law
- Forces between Multiple Charges
- Electric Field
- Electric Field Due to a System of Charges
- Physical Significance of Electric Field
- Electric Field Lines
- Electric Flux
- Electric Dipole
- Dipole in a Uniform External Field
- Continuous Charge Distribution
- Gauss’s Law
- Application of Gauss' Law
Current Electricity
Electrostatic Potential and Capacitance
- Electric Potential and Potential Energy
- Electrostatic Potential
- Electric Potential Due to a Point Charge
- Potential Due to an Electric Dipole
- Potential due to a System of Charges
- Equipotential Surfaces
- Relation Between Electric Field and Electrostatic Potential
- Potential Energy of a System of Charges
- Potential Energy of a Single Charge
- Potential Energy of a System of Two Charges in an External Field
- Potential Energy of a Dipole in an External Field
- Electrostatics of Conductors
- Dielectrics and Polarisation
- Capacitors and Capacitance
- The Parallel Plate Capacitor
- Effect of Dielectric on Capacitance
- Combination of Capacitors
- Energy Stored in a Charged Capacitor
Magnetic Effects of Current and Magnetism
Current Electricity
- Electric Current
- Electric Currents in Conductors
- Ohm's Law
- Drift of Electrons and the Origin of Resistivity
- Mobility of Electrons
- Limitations of Ohm’s Law
- Resistivity of Various Materials
- Temperature Dependence of Resistivity
- Electrical Energy and Power in Conductors
- Cells, EMF, and Internal Resistance
- Cells in Series and in Parallel
- Kirchhoff’s Laws
- Wheatstone Bridge
Moving Charges and Magnetism
- Electromagnetism
- Magnetic force
- Motion in a Magnetic Field
- Magnetic Field Due to a Current-carrying Conductor: Biot-savart's Law
- Applications of Biot-Savart's Law > Magnetic Field at the Axis of a Circular Current-carrying Loop
- Ampere’s Circuital Law
- Solenoid
- Force Between Two Parallel Currents (Ampere’s Law)
- Torque on a Rectangular Current Loop in a Uniform Magnetic Field
- Circular Current Loop as a Magnetic Dipole
- Moving Coil Galvanometer
- Kirchhoff’s Laws
Electromagnetic Induction and Alternating Currents
Electromagnetic Waves
Magnetism and Matter
Optics
Electromagnetic Induction
Alternating Current
Dual Nature of Radiation and Matter
Atoms and Nuclei
Electromagnetic Waves
Electronic Devices
Ray Optics and Optical Instruments
- Ray Optics Or Geometrical Optics
- Reflection of Light by Spherical Mirrors
- Sign Convention for Reflection by Spherical Mirrors
- Focal Length of Spherical Mirrors
- Mirror Equation of Spherical Mirrors
- Refraction of Light
- Total Internal Reflection
- Applications of Total Internal Reflection
- Refraction at a Spherical Surfaces
- Refraction by a Lens
- Power of a Lens
- Combined Focal Length of Two Thin Lenses in Contact
- Refraction of Light through a Prism
- Introduction to Optical Instruments
- Microscope and it’s types
- Telescope
Wave Optics
- Introduction to Wave Optics
- Huygens Principle
- Refraction of a Plane Wave
- Refraction at a Rarer Medium
- Reflection of a Plane Wave by a Plane Surface
- Coherent and Incoherent Addition of Waves
- Interference of Light Waves and Young’s Experiment
- Diffraction of Light
- The Single Slit
- Seeing the Single Slit Diffraction Pattern
- Polarisation of Light
Communication Systems
Dual Nature of Radiation and Matter
- Understanding Dual Nature of Radiation and Matter
- Electron Emission
- Photoelectric Effect - Hertz’s Observations
- Photoelectric Effect - Hallwachs’ and Lenard’s Observations
- Experimental Study of Photoelectric Effect
- Effects of Intensity and Frequency on Photocurrent
- Photoelectric Effect and Wave Theory of Light
- Einstein’s Photoelectric Equation: Energy Quantum of Radiation
- Particle Nature of Light: The Photon
- Wave Nature of Matter
The Special Theory of Relativity
Atoms
Nuclei
Semiconductor Electronics - Materials, Devices and Simple Circuits
Communication Systems
- Detection of Amplitude Modulated Wave
- Production of Amplitude Modulated Wave
- Basic Terminology Used in Electronic Communication Systems
- Sinusoidal Waves
- Modulation and Its Necessity
- Amplitude Modulation (AM)
- Need for Modulation and Demodulation
- Satellite Communication
- Propagation of EM Waves
- Bandwidth of Transmission Medium
- Bandwidth of Signals
The Special Theory of Relativity
- The Special Theory of Relativity
- The Principle of Relativity
- Maxwell'S Laws
- Kinematical Consequences
- Dynamics at Large Velocity
- Energy and Momentum
- The Ultimate Speed
- Twin Paradox
Estimated time: 7 minutes
CBSE: Class 12
Core Idea: Electrostatic Analog
The field of a bar magnet at large distances can be obtained from the field of an electric dipole by making the following replacements:
| Electrostatics | Magnetism |
|---|---|
| Electric field E | Magnetic field B |
| Electric dipole moment p | Magnetic dipole moment m |
| \[\frac {1}{4πϵ_0}\] | \[\frac {μ_0}{4π}\] |
Replacement Rule
- Replace E by B
- Replace p by m
- Replace \[\frac {1}{4πϵ_0}\] by \[\frac {μ_0}{4π}\]
For a short bar magnet, the magnetic field on the equatorial line is:
Beq = −\[\frac {μ_0}{4π}\]\[\frac {m}{r^3}\]
The negative sign indicates that the direction of the field is opposite to the magnetic dipole moment vector.
For a short bar magnet, the magnetic field on the axial line is:
Bax = \[\frac {μ_0}{4π}\]\[\frac {m}{r^3}\]
This field is along the direction of the dipole moment vector.
CBSE: Class 12
The Dipole Analogy
CBSE: Class 12
Example
Step 1: Understand the setup
- There are two identical magnetic needles (dipoles): P at O (fixed) and Q placed at different positions around P.
- Each position of Q (Q₁, Q₂, …, Q₆) has its own direction of magnetic moment mQ.
Step 2: Recall field directions of P
Use the magnetic dipole field rules for P:
- On the axial line of P: BP is along mP.
- On the equatorial line of P: BP is opposite to mP.
Step 3: Use the equilibrium rule
For Q in the field of P:
- If mQ is parallel to BP → equilibrium is stable (minimum potential energy).
- If mQ is antiparallel to BP → equilibrium is unstable (maximum potential energy).
- If mQ is neither parallel nor antiparallel → not in equilibrium (net torque not zero).
Step 4: Check each configuration (using the rule)
Not in equilibrium:
- Configurations PQ1 and PQ2 (because mQ is not along or opposite to BP).
Stable equilibrium:
- Configurations PQ3 and PQ6 (here mQ is parallel to BP).
Unstable equilibrium:
- Configurations PQ5 and PQ4 (here mQ is antiparallel to BP).
Step 5: Lowest potential energy configuration
- Lowest potential energy happens when mQ is parallel to BP and the angle is zero.
- Among all shown positions, this is configuration PQ6, so PQ6 has the lowest potential energy.
