Electric Charges: Properties, Conservation, Coulomb’s Law & Applications

What is Electric Charge?

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of charges:

• Positive charge (+q): Gained when electrons are removed.
• Negative charge (−q): Gained when electrons are added.

Key fact: Charges cannot be created or destroyed; they can only be transferred (conservation of charge).

How Charges Interact

• Like charges repel: Two positive or two negative charges push each other away.
• Unlike charges attract: A positive and a negative charge pull each other together.

Example: Rubbing a plastic rod with wool transfers electrons, making the rod negatively charged. It attracts small pieces of paper (which are neutral).

Conservation of Charge

The total charge in an isolated system remains constant. This is called charge conservation.

Example: When you comb your hair, electrons move from your hair to the comb. Your hair becomes positively charged, and the comb becomes negatively charged. The total charge before and after remains zero.

Coulomb’s Law

Coulomb’s law describes the force between two point charges. The formula is:

$$F=k_e\frac{|q_1{q}_2|}{r^2}$$

Where:

• $F$ = electrostatic force (in newtons, N)
• $k_e$ = Coulomb’s constant ($9\times 10^9{\text{N m}}^2/{\text{C}}^2$)
• $q_1,q_2$ = charges (in coulombs, C)
• $r$ = distance between charges (in meters, m)

Direction of force:

• If charges are opposite, force is attractive (toward each other).
• If charges are same, force is repulsive (away from each other).

Solved Example

Two charges, $q_1=+3\mu \text{C}$ and $q_2=-5\mu \text{C}$, are placed 10 cm apart. Find the force between them.

Solution:

1. Convert charges to coulombs: $3\mu \text{C}=3\times 10^{-6}\text{C}$ $-5\mu \text{C}=-5\times 10^{-6}\text{C}$
2. Distance $r=10\text{cm}=0.1\text{m}$.
3. Use Coulomb’s law: $$F=9\times 10^9\times \frac{|3\times 10^{-6}\times (-5\times 10^{-6})|}{(0.1{)}^2}$$ $$F=9\times 10^9\times \frac{15\times 10^{-12}}{0.01}=13.5\text{N}$$
4. Since charges are opposite, the force is attractive.

Conductors and Insulators

Why do charges move to the surface? In conductors, free electrons repel each other and spread out until they are as far apart as possible (the surface).

Applications of Electric Charges

1. Photocopiers: Use static electricity to transfer toner (charged ink) onto paper.
2. Lightning rods: Protect buildings by safely conducting lightning (a giant electric spark) into the ground.
3. Electrostatic precipitators: Remove dust and smoke from factory exhausts using charged plates.
4. Inkjet printers: Tiny charged droplets of ink are deflected by electric fields to print precise patterns.

NEB Board-Style Questions

Short Answer (5 marks)

1. Explain why a charged plastic rod attracts small pieces of paper even when the paper is uncharged.
2. Two point charges $q_1=+4\mu \text{C}$ and $q_2=-2\mu \text{C}$ are 5 cm apart. Calculate the force between them. What is the nature of the force?

Long Answer (10 marks)

3. Derive Coulomb’s law from the given formula. Explain how the force changes if:
   • The distance between charges is doubled.
   • One charge is tripled while the other remains the same.
4. Distinguish between conductors and insulators with examples. Why are conductors used in electrical wiring?

Exam Tip

• Memorize Coulomb’s law formula and units.
• Practice charge interaction diagrams: Draw arrows to show attraction/repulsion.
• Understand conservation of charge: Total charge before and after any process must be equal.
• Application-based questions are common—link theory to real-world examples (e.g., photocopiers, lightning rods).

Visual Summary:

flowchart TD
    A["Electric Charge"] --> B["Types: +ve, -ve"]
    A --> C["Conservation: Total charge is constant"]
    A --> D["Coulomb's Law: F = k q1q2/r²"]
    D --> E["Attraction/Repulsion"]
    A --> F["Conductors vs Insulators"]
    F --> G["Conductors: Charges move freely"]
    F --> H["Insulators: Charges fixed"]
    A --> I["Applications: Photocopiers, Lightning Rods"]