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
- Overview: Electric Potential
- Overview: Capacitors and Dielectrics
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
- Overview: Electric Resistance and Ohm's Law
- Overview: DC Circuits and Measurements
Magnetic Effects of Current and Magnetism
Moving Charges and Magnetism
- Electromagnetism
- Magnetic force
- Motion in a Magnetic Field
- 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
- Overview: Moving Charges and Magnetic Field
- Overview: Torque on a Current-Loop : Moving-Coil Galvanometer
Electromagnetic Induction and Alternating Currents
Magnetism and Matter
- Concept of Magnetism
- The Bar Magnet
- Magnetic Field Lines
- Bar Magnet as an Equivalent Solenoid
- The Dipole in a Uniform Magnetic Field
- The Electrostatic Analog
- Magnetism and Gauss’s Law
- Magnetisation and Magnetic Intensity
- Magnetic Properties of Materials
- Overview: Magnetism and Mater
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
Dual Nature of Radiation and Matter
- Dual Nature of Radiation
- 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
The Special Theory of Relativity
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: 8 minutes
CBSE: Class 12
Introduction
In earlier sections, the source of the electric field was known — the charges and their locations were specified. Now the focus shifts to a charge q placed in an externally created electric field.
Key distinction:
- The external field E and potential V are created by other source charges (not by q itself)
- Charge q is assumed to be small enough that it does not disturb the original field
- The source charges are fixed (not affected by q)
CBSE: Class 1
Definition: Potential Energy of a Single Charge
The potential energy of a charge q placed at a point with external electric potential V(r) is equal to the work done in bringing the charge from infinity to that point against the external field.
CBSE: Class 12
Derivation (Step-by-Step)
| Step | Statement | Reasoning |
|---|---|---|
| 1 | Place an external potential V in space | Other charges create the field; it is not disturbed by q. |
| 2 | Potential at infinity = 0 | Standard reference convention |
| 3 | Work done to bring a unit positive charge from ∞ to (P = V(P)) | Definition of electric potential |
| 4 | Work done to bring a charge (q) from ∞ to point r = qV(r) | Scales by a factor of q |
| 5 | This work is stored as potential energy | Electrostatic force is conservative |
| Result | U(r) = qV(r) | Final expression |
CBSE: Class 12
Formula: Potential Energy of a Single Charge
U(r) = qV(r)
where:
- U(r) = Potential energy of the charge at position r (in Joules, J)
- q = Charge of the particle (in Coulombs, C)
- V(r) = External electric potential at position r (in Volts, V)
- r = Position vector of the point from the origin
| Quantity | Symbol | SI Unit | Dimensional Formula |
|---|---|---|---|
| Potential Energy | U | Joule (J) | [ML2T−2] |
| Charge | q | Coulomb (C) | [AT] |
| Electric Potential | V | Volt (V) | [ML2T−3A−1] |
CBSE: Class 12
Special Case: The Electron Volt (eV)
When the charge is an electron (q = e = 1.6 × 10−19 C), and it is accelerated through a potential difference of 1 Volt, the energy gained is:
U = qV = (1.6 × 10−19 C) × (1 V) = 1.6 × 10−19 J = 1 eV
eV Conversion Table
| Unit | Relation to eV | Value in Joules |
|---|---|---|
| 1 eV | 1 electron volt | 1.6 × 10−19 J |
| 1 keV | 103 eV | 1.6 × 10−16 J |
| 1 MeV | 106 eV | 1.6 × 10−13 J |
| 1 GeV | 109 eV | 1.6 × 10−10 J |
| 1 TeV | 1012 eV | 1.6 × 10−7 J |
CBSE: Class 12
Real-Life Analogy
Gravity vs. Electricity (Analogy)
Just as a mass m has gravitational PE = mgh in a gravitational field, a charge q has electrostatic PE = qV in an electric field.
| Concept | Gravity | Electrostatics |
|---|---|---|
| Field agent | Gravitational field g | Electric field E |
| Potential | Gravitational potential | Electric potential V |
| Potential Energy | U=mghU=mgh | U = qV |
| Reference level | Ground (h = 0) | Infinity (V = 0) |
