Overview
This lecture covers "Electric Charges and Fields," focusing on foundational concepts, key laws, properties, mathematical derivations, and common exam questions in physics.
Division of Electrostatics and Electrodynamics
- The first two chapters deal with electrostatics (study of stationary charges).
- Electrodynamics studies moving charges (current), covered in later chapters.
Electric Charge: Concepts and Properties
- Electric charge is a property that produces an electric field around it.
- Charges are of two types: positive (more protons, fewer electrons) and negative (more electrons, fewer protons).
- Conductors have free charges allowing flow; insulators do not.
- Like charges repel; unlike charges attract (fundamental law of electrostatics).
- Charge can be transferred, not created or destroyed (conservation).
- Charge is quantized: ( q = n e ), where ( n ) is an integer.
Electrostatic Induction and Gold Leaf Electroscope
- Electrostatic induction: a charged body can attract an uncharged one but cannot repel it.
- Gold Leaf Electroscope detects the presence of charge but not its type.
Properties of Charge
- Additivity: Net charge is the algebraic sum of individual charges.
- Conservation: Total charge in an isolated system is constant.
- Quantization: Charge exists as multiples of the elementary charge (( e )).
Coulomb’s Law
- Force between two point charges: ( F = k \frac{q_1 q_2}{r^2} ).
- ( k ) (electrostatic constant) depends on medium: ( k = \frac{1}{4\pi\epsilon_0} ).
- For air/vacuum: ( k = 9 \times 10^9 ,\text{N m}^2/\text{C}^2 ).
- Force is directly proportional to product of charges, inversely to square of distance.
Electric Field and Its Calculations
- Electric field (( E )): region around a charge where force is exerted on another charge.
- ( E = F/q_0 ) (force per unit positive test charge).
- Test charge should be small and positive.
- SI unit: ( \text{N/C} ).
- Direction: from positive to negative charge.
- Electric field due to point charge: ( E = k \frac{q}{r^2} ).
Electric Dipole and Dipole Moment
- Electric dipole: two equal, opposite charges separated by a distance.
- Dipole moment (( p )): ( p = q \times 2a ); unit: ( \text{C m} ); direction: negative to positive.
- Electric field on axis (axial): ( E = \frac{2kp}{r^3} ).
- Electric field on perpendicular bisector (equatorial): ( E = \frac{kp}{r^3} ).
Torque on a Dipole in Electric Field
- Torque (( \tau )): ( \tau = pE \sin\theta ).
- Maximum when ( \theta = 90^\circ ); zero when dipole aligns with field.
- Stable equilibrium at ( \theta = 0^\circ ); unstable at ( \theta = 180^\circ ).
Electric Field Lines and Their Properties
- Imaginary lines representing field direction and strength.
- Emerge from positive, end at negative charges.
- Never intersect or form closed loops.
- Density indicates field strength.
- No field lines inside a conductor (electrostatic shielding).
Electric Flux and Gauss’s Law
- Electric flux (( \Phi_E )): ( \Phi_E = E \cdot A ) or ( \Phi_E = \oint \vec{E} \cdot d\vec{A} ).
- SI unit: ( \text{N m}^2/\text{C} ); scalar quantity.
- Gauss’s Law: total flux through a closed surface equals enclosed charge divided by permittivity (( \Phi_E = \frac{q_{enc}}{\epsilon_0} )).
- Gauss’s Law aids in calculation of fields for symmetrical charge distributions like spheres, sheets, and wires._
Key Terms & Definitions
- Electrostatics — study of stationary charges and their effects.
- Electrodynamics — study of moving charges (current).
- Conductors — materials that allow charge to move freely.
- Electric Field — region where a charge experiences force from another charge.
- Dipole Moment — product of charge and separation, direction from negative to positive.
- Electric Flux — measure of the number of electric field lines passing through a surface.
- Gauss’s Law — total electric flux through a closed surface is equal to charge enclosed divided by ( \epsilon_0 ).
- Electrostatic Shielding — property that prevents electric field penetration inside a conductor.
Action Items / Next Steps
- Review derivations for electric field due to point charge, dipole (axial/equatorial), torque, and Gauss’s law.
- Practice MCQs, assertion-reason, and calculation-based problems from the lecture.
- Complete assigned homework and attempt unsolved textbook questions.
- Prepare summary notes for formulas and SI units for quick revision.