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: 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 12
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) |
