Electrostatics: Fundamentals, Charge Conservation, and Coulomb's Law

Definition of Electrostatics: The study of stationary charges.
Fundamental Concepts of Matter:
- Matter: Defined as anything which occupies space and has mass.
- Atoms: Identified as the smallest unit of matter.

Composition of Atoms: Atoms consist of three subatomic particles:
- Protons: Positively charged ( $+$ ).
- Electrons: Negatively charged ( $-$ ).
- Neutrons: Neutral/Zero charge ( $0$ ).
Charge Values:
- An electron has a charge of $-1.6 \times 10^{-19}\,C$ .
- A proton has a charge of $+1.6 \times 10^{-19}\,C$ .

Representation: Charge is represented by the symbol $Q$ .
Standard Unit: Charge is measured in Coulombs ( $C$ ).
Conversion Units:
- Milli-Coulomb ( $mC$ ) = $\times 10^{-3}\,C$
- Micro-Coulomb ( $\mu C$ ) = $\times 10^{-6}\,C$
- Nano-Coulomb ( $nC$ ) = $\times 10^{-9}\,C$
- Pico-Coulomb ( $pC$ ) = $\times 10^{-12}\,C$

The Charging Process: An object becomes charged by gaining or losing electrons.
Charge by Friction: Electrons are transferred when the surfaces of materials are rubbed together.
- Triboelectric Charging: This specific process of charging an object through friction is known as triboelectric charging.
- Example: Rubbing a ruler on a cloth made of wool causes the ruler to gain electrons ( $e^-$ ) as they move from the cloth to the ruler.
Material States:
- Negatively Charged: A material that has gained electrons, resulting in an excess of electrons.
- Positively Charged: A material that has lost electrons, resulting in a deficiency of electrons.

Polarizing Neutral Objects: When a negatively charged ruler is placed over pieces of neutral paper, the ruler induces polarity in the paper.
- Mechanism: The negative charge of the ruler repels electrons within the paper and attracts the positive components.
- Result: The paper becomes polarized (one end is positive, the other negative), and the positive side is attracted to the ruler.
Interaction with Water:
- Observation: If a charged ruler is placed next to a stream of water from a tap, the stream moves towards the ruler.
- Explanation: Water is a polar molecule ( $\delta^-$ , $\delta^+$ ). The charged ruler attracts the polar water molecules.

Basic Interaction Rules:
- Opposite charges attract ( $+ \rightarrow \leftarrow -$ ): They move towards each other.
- Like charges repel ( $+ \leftarrow \rightarrow +$ or $- \leftarrow \rightarrow -$ ): They move away from each other.
Net Charge ( $Q_{net}$ ): Represents the total amount of charge in a given system.
- Formula: $Q_{net} = Q_{1} + Q_{2} + Q_{3} ...$
- Example: If $Q_{A} = -2.5\,\mu C$ and $Q_{B} = -3.8\,\mu C$ , then $Q_{net} = -2.5 \times 10^{-6} + (-3.8 \times 10^{-6}) = -6.3 \times 10^{-6}\,C$ .
Law of Conservation of Charge: In an isolated system, the net charge remains the same after any physical change.
- Charge Sharing: When two charges in an isolated system come into contact, charge is equally shared as electrons move from high concentration to low concentration.
- New Charge Calculation: After separation, spheres will have the same amount of charge.
- Formula: $Q_{new} = \frac{Q_{1} + Q_{2}}{2}$
- Example Calculation: If $Q_{1} = 4.2 \times 10^{-3}\,C$ and $Q_{2} = -7.5 \times 10^{-3}\,C$ , then $Q_{new} = \frac{4.2 \times 10^{-3} + (-7.5 \times 10^{-3})}{2} = -1.65 \times 10^{-3}\,C$ .

Direction of Electron Transfer:
- From a less positive/more negative object to a more positive/less negative object.
- Example 1: From A ( $+3.2$ ) to B ( $+7.5$ ).
- Example 2: From B ( $-8.4$ ) to A ( $-2.7$ ).
Principle of Charge Quantization: Every charge in the universe is an integer multiple of the electron charge.
- Formula: $Q = n \times q_{e}$
- Variables:
  - $n$ = number of electrons
  - $q_{e} = -1.6 \times 10^{-19}\,C$
Calculating Transferred Electrons:
1. Step 1: Calculate the amount of charge transferred ( $Q_{transferred} = Q_{new} - Q_{old}$ ).
2. Step 2: Apply the quantization formula ( $n = \frac{Q_{transferred}}{q_{e}}$ ).
- Sample Calculation:
  - Initial charges: $Q_{A} = -2.8\,\mu C$ , $Q_{B} = +7.2\,\mu C$
  - $Q_{new} = \frac{-2.8 \times 10^{-6} + 7.2 \times 10^{-6}}{2} = 2.2 \times 10^{-6}\,C$
  - $Q_{transferred} = 2.2 \times 10^{-6} - (-2.8 \times 10^{-6}) = 5 \times 10^{-6}\,C$
  - $n = \frac{5 \times 10^{-6}}{1.6 \times 10^{-19}} = 3.125 \times 10^{13}$ electrons.

Electrostatic Force: Charges exert a force on each other (attraction or repulsion).
Definition: The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Notation: $F \propto \frac{Q_{1} Q_{2}}{r^2}$ .