Overview
This lecture covered the core concepts, definitions, derivations, and key competency-based questions related to the chapter "Electric Charges and Fields" in physics, with a focus on both theory and exam-type problems.
Division of Electrostatics
- Electrostatics studies electric charges at rest; electrodynamics covers charges in motion (current).
- The first two chapters in Class 12 Physics fall under electrostatics.
- Electric charge creates an electric field and is of two types: positive (more protons) and negative (more electrons).
Properties and Detection of Charge
- Charge is quantized (exists in discrete multiples of the electron charge, e = 1.6 × 10⁻¹⁹ C).
- The SI unit of charge is the coulomb (C).
- Like charges repel; unlike charges attract.
- Conductors allow free movement of charge; insulators do not.
- Gold (or aluminum) leaf electroscope detects the presence of charge through electrostatic induction.
Basic Properties of Charge
- Additivity: Total charge in a system is the algebraic sum of individual charges.
- Conservation: Charge cannot be created or destroyed, only transferred.
- Quantization: Charge is always in integer multiples of elementary charge (Q = n·e).
Coulomb’s Law & Constants
- The electrostatic force F = k·q₁·q₂/r², where k = 1/(4πε₀), and ε₀ is the permittivity of free space (8.85 × 10⁻¹² C²/N·m²).
- For vacuum, k ≈ 9 × 10⁹ N·m²/C².
- Force is inversely proportional to the square of the distance between charges.
Electric Field
- Electric field (E) is the force experienced per unit positive test charge: E = F/q₀.
- E for a point charge: E = k·q/r².
- Electric field lines originate from positive charges and end on negative charges; they never intersect.
Electric Dipole
- An electric dipole consists of two equal and opposite charges separated by distance 2a.
- Dipole moment (p) = q·2a, direction from negative to positive.
- SI unit of dipole moment: coulomb-meter (C·m).
Electric Field of a Dipole
- On the axial point: E = (2kp)/r³ (for short dipole, r >> a).
- On the equatorial point: E = (-kp)/r³ (for short dipole).
- Ratio of axial to equatorial field magnitude is 2:1 for short dipole.
Torque on a Dipole in Uniform Electric Field
- Torque (τ) = pE·sinθ, where θ is the angle between p and E.
- τ is maximum when θ = 90°, zero when θ = 0° or 180°.
- Equilibrium: stable at θ = 0°, unstable at θ = 180°.
Electric Flux and Gauss’s Law
- Electric flux (Φ) = E·A·cosθ; measures field lines passing through area A.
- Gauss’s Law: total flux through a closed surface = net charge enclosed/ε₀.
- Used to derive fields of symmetric charge distributions (sphere, sheet, wire).
Applications of Gauss’s Law
- Infinite line of charge: E = λ/(2πε₀r), where λ is linear charge density.
- Infinite sheet: E = σ/(2ε₀), σ is surface charge density.
- Conducting sphere: Outside, E = (1/4πε₀)·Q/r²; at surface, E = σ/ε₀; inside, E = 0.
Key Terms & Definitions
- Electrostatics — Study of stationary electric charges.
- Permittivity (ε₀) — Ability of a medium to permit electric field lines; for free space, ε₀ = 8.85 × 10⁻¹² C²/N·m².
- Electric Dipole — Two equal and opposite charges separated by a distance.
- Dipole Moment (p) — Vector quantity, p = q·2a, points from negative to positive charge.
- Electric Flux (Φ) — Measure of electric field lines passing through a surface.
- Gauss’s Law — The net flux through a closed surface equals the net charge enclosed divided by ε₀.
Action Items / Next Steps
- Review all key formulas and concepts before attempting competency-based questions.
- Complete assigned homework and practice questions, especially those on torque, flux, and electric field.
- Read Chapter 1 of Class 12 Physics (Electric Charges and Fields) from NCERT.
- Prepare questions on derivations and diagrams for the next session.