Topics
Electric Charges and Fields
- Electric Charge
- Conductors and Insulators
- Basic 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
Electrostatics
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
Current Electricity
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
Magnetic Effects of Current and Magnetism
Moving Charges and Magnetism
- Electromagnetism
- Magnetic force
- Motion in a Magnetic Field
- Magnetic Field Due to a Current Element, Biot-savart Law
- Magnetic Field on 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
Electromagnetic Induction and Alternating Currents
Magnetism and Matter
Electromagnetic Waves
Optics
Electromagnetic Induction
Dual Nature of Radiation and Matter
Alternating Current
- AC Voltage Applied to a Resistor
- Representation of AC Current and Voltage by Rotating Vectors - Phasors
- AC Voltage Applied to an Inductor
- AC Voltage Applied to a Capacitor
- AC Voltage Applied to a Series LCR Circuit
- Phasor-diagram Solution
- Resonance
- Power in AC Circuit
- Transformers
- Overview: AC Circuits
Atoms and Nuclei
Electromagnetic Waves
- Concept of Electromagnetic Waves
- Displacement Current
- Sources of Electromagnetic Waves
- Nature of Electromagnetic Waves
- Electromagnetic Spectrum
- Overview of 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
- Optical Instruments
- Microscope and it’s types
- Telescope
- Overview of Ray Optics and Optical Instruments
Communication Systems
Wave Optics
- Concept of 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
- Overview: Wave Optics
The Special Theory of Relativity
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
- Overview: Dual Nature of Radiation and Matter
Atoms
Nuclei
- Atomic Masses and Composition of Nucleus
- Size of the Nucleus
- Mass - Energy
- Nuclear Binding Energy
- Nuclear Force
- Radioactivity
- Forms of Energy > Nuclear Energy
- Nuclear Fission
- Nuclear Fusion
- Controlled Thermonuclear Fusion
- Overview: Nuclei
Semiconductor Electronics - Materials, Devices and Simple Circuits
- Concept of Semiconductor Electronics
- Classification of Metals, Conductors and Semiconductors
- Intrinsic Semiconductor
- Extrinsic Semiconductor
- n-type Semiconductor
- p-type Semiconductor
- Diode or p-n Junction
- Semiconductor Diode
- Application of Junction Diode as a Rectifier
- Overview: Semiconductor Electronics
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
Definition: Magnetic Dipole
A magnetic dipole is a system consisting of two equal and opposite magnetic poles separated by a small distance. Any small current loop, a bar magnet, or a compass needle acts as a magnetic dipole.
CBSE: Class 12
Torque on a Magnetic Dipole
Torque is the rotational force that tends to align the magnetic dipole along the direction of the external magnetic field.
τ = m × B
In magnitude:
τ = m B sin θ
where θ is the angle between m and B.
CBSE: Class 12
Derivation of Potential Energy
Work Done = Change in Potential Energy
When the dipole rotates from angle θ1 to θ2, work is done against the torque of the field.
dW = τ dθ = m B sin θ dθ
Integrating from the reference position θ = 90° to angle θ:
W = \[\int_{90°}^\theta mB\sin\theta^{\prime}d\theta^{\prime}\]
W = \[mB\left[-\cos\theta^{\prime}\right]_{90^{\circ}}^\theta\]
W = mB(−cos θ + cos 90°)
Um = W = −mB cos θ = −m⋅B
θ = 90° as a reference:
The reference is chosen so that Um = 0 when θ = 90° (dipole perpendicular to field), making calculations consistent and symmetric.
The reference is chosen so that Um = 0 when θ = 90° (dipole perpendicular to field), making calculations consistent and symmetric.
CBSE: Class 12
Example
Part (a) – Cutting a Bar Magnet
Q: What happens when you cut a bar magnet into two pieces?
Answer: Whether you cut it across its width or along its length, you always get two smaller magnets, each with its own north and South pole. You can never isolate a single pole.
Part (b) - Compass Needle in a Uniform Field
Q: Why does a compass needle feel a turning force but no pulling force in a uniform field, while an iron nail near a magnet feels both?
Answer:
- In a uniform field, both poles of the needle feel equal but opposite forces → they cancel out → no net pull, but they still cause a twist (torque).
- Near a bar magnet, the field is uneven (stronger near the poles) → forces on the two poles of the nail are unequal → nail gets pulled in AND twisted. The nail is also attracted because the magnet induces poles in it.
Part (c) - A Magnet Have No Poles
Q: Must every magnetic object have a north and south pole?
Answer: No. Some special shapes — like a toroid (donut-shaped coil) or an infinitely long straight wire — have zero net magnetic moment. Their field loops close on themselves with no identifiable poles.
Part (d) - Which Bar is the Magnet?
Q: You have two bars — one is a magnet, one is plain iron. Using only these two bars, how do you find out which is which?
Answer: Bring one bar's middle point close to the end of the other bar.
- If it attracts strongly → the bar you brought close is the magnet (its pole is near the iron).
- If there is little or no pull → the bar being tested is the magnet (its midpoint/equatorial region has a weak field).
- Also, only a magnet can repel another magnet — attraction alone can't confirm magnetism, but repulsion always can.
