Electric Charges and Fields Study Notes

Common experiences of electric discharge:
- Sparks or crackles when removing synthetic clothes, especially in dry weather.
- Lightning during thunderstorms, experienced as a sensation of electric shock.
These phenomena are due to discharge of accumulated electric charges from rubbing insulating surfaces, related to static electricity.
Static electricity: Refers to charges that do not move or change with time.
Electrostatics: The study of forces, fields, and potentials arising from static charges.

Historically, charges were discovered through Thales of Miletus, Greece (~600 BC) with amber attracting light objects when rubbed with wool/silk.
Several pairs of materials can attract light objects upon rubbing, revealing the nature of charge interactions:
  - Glass rods rubbed with wool/silk repel each other.
  - Two plastic rods rubbed with cat’s fur repel each other.
  - Glass rod attracts wool and repels cat’s fur.
Electric Charge Types:
  - Two types of electric charges exist:
    1. Positive charge – associated with glass rod or cat’s fur.
    2. Negative charge – associated with plastic rod or silk.
  - Polarity of Charge: Differentiates two charge types where like charges repel and unlike charges attract.
When two electrified bodies contact, their charges neutralize. Benjamin Franklin conventionally named:
- Glass rod/cat’s fur charge as positive (+)
- Plastic rod/silk charge as negative (−)
An object is electrified if it has an electric charge; it’s electrically neutral if it has no charge.

Gold-leaf electroscope: detects charge via a vertical metal rod in a box with thin gold leaves attached to the bottom.
When a charged object contacts the metal knob, charge spreads to the leaves, causing them to diverge. The degree of divergence indicates charge amount.
Charge Induction: Material bodies acquire charge through electron movement.
Conductors vs Insulators:
- Conductors allow electricity to pass (metals, human bodies).
- Insulators resist electricity (glass, nylon, wood).
Electrons, which are loosely bound in atoms, transfer between bodies during charging.
Charging Mechanism:
- Positively charged by losing electrons.
- Negatively charged by gaining electrons (e.g., glass rod rubbed with silk).

Two basic charges exist: positive and negative. Their effects cancel out.
1.4.1 Additivity of Charges:
- Charges are scalars and can be algebraically summed.
- Total charge of multiple charges: $q_{total} = q_1 + q_2 + … + q_n$ .
1.4.2 Charge Conservation:
- In any isolated system, charge is conserved; no net charge can be created or destroyed.
1.4.3 Quantisation of Charge:
  - Total charge $q$ on a body is an integral multiple of basic charge unit $e$ : $q = n imes e ext{, where } n ext{ is an integer}$ .
  - Charge on an electron: $-e$ ; charge on a proton: $+e$ .
  - SI unit of charge: coulomb (C).
  - Charge magnitude: $e ext{ } hickapprox 1.602 imes 10^{-19} C$ .
  - Charges like $1 ext{ } ext{μC} = 10^{-6} ext{ }C$ and $1 ext{ } ext{mC} = 10^{-3} ext{ }C$ appear in practical applications.
  - Observation: Charge appears continuous at macroscopic levels due to large multiples of $e$ .

Coulomb's Law: Quantitatively describes the force between two point charges:
  - $F = k rac{q_1 imes q_2}{r^2} ext{ where } r ext{ is the distance between charges}$ .
  - Measured by a torsion balance.
  - At distance $r$ : the force varies inversely with the square of the distance and is proportional to the product of charges.
Experimental application: established at a macroscopic scale and confirmed through subatomic measurements.
Constant k: Approximately equals $9 imes 10^9 rac{N ext{m}^2}{C^2}$ in SI units.

For two charges $q_1$ and $q_2$ separated by distance $r$ , the vector notation is:
$F_{21} = k rac{q_1 imes q_2}{r^2} ext{ (vector form incorporating direction)}$ .

Electric force follows the same inverse square law as gravitational force.
Detailed calculations and examples to show the relative strength of these forces.

Demonstrate through specific values of electric and gravitational forces that electric forces are considerably stronger (with calculations).

Review of the concept of an electric field created by a point charge (
$Q$ ) and its effects on test charges (
$q$ ) placed at various distances.
Electric field due to charge (
$Q$ ) at distance
$r$ :
$E( ext{r}) = k rac{Q}{r^2}$ and the proportional relationship to the force on charge
$q$ placed in its vicinity.
Important properties of electric field vectors:
- Magnitude and direction vary with point in space.

Habits of electric field lines based on charge configurations. Characteristics and rules for field lines:
  1. Start from positive charges and end at either negative charges or infinity.
  2. Density indicates strength, and lines can never intersect.
  3. No closed loops in electrostatics.

Define electric flux (flux through an area element), including the vector definition and practical derivation of its overall effect through surfaces.
The concept of flux illustrates the strength of electric fields across surfaces, allowing specific calculations through defined integrals.

Characterization of electric dipoles including their properties and influence on electric fields.
Analysis of electric fields both in dipole axes and equatorial planes, with mathematically defined functions.

Classify charge distribution concepts into linear, surface, and volume densities determined by concepts of integration.
Define basis for calculating electric fields from continuous charge distributions analogously to discrete charges.

Review of Gauss’s Law with experiments demonstrating its validity. Properties used in fields of symmetry.
Examples analyzing different charge configurations (straight wire, infinite plane, spherical shell) using Gauss's Law to derive their electric fields effectively.

Review key points on electric properties, charge behaviours, and electric field implications throughout various systems and configurations.
Reinforcement of Gauss's Law applications and continuous charge distributions, with practical summaries of findings.

Engage students with practical problems that reinforce concepts of electric charges, Coulomb’s Law, field line behaviours, and applications of Gauss's Law across varied configurations. Each task requires thorough calculations and understanding of electrostatic principles.