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
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.
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.
In magnitude:
where θ is the angle between m and B.
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.
Integrating from the reference position θ = 90° to angle θ:
The reference is chosen so that Um = 0 when θ = 90° (dipole perpendicular to field), making calculations consistent and symmetric.
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.
