Electric Charge and Electrostatics

Introduction

• Electric charge: a physical property that causes matter to experience a force when placed in an electromagnetic field.
• Electrically charged objects can be obtained by:
  • Friction: rubbing objects together (e.g., comb and hair, silk and glass)
  • Conduction: contact with another charged object
  • Induction: influence of a nearby charged object

Types of Electric Charges

• Positive and Negative Charges:
  • Like charges repel, unlike charges attract.
  • Positive charge: deficit of electrons.
  • Negative charge: surplus of electrons.

Electrostatics

• Study of electric charges at rest.
• Key phenomena:
  • Electrification by friction, conduction, and induction.
  • Nullification of charges when oppositely charged objects come in contact.

Gold-leaf Electroscope

• Device to detect electric charge.
• Consists of insulated metal rod, gold leaves, and a metal disc.
• Charged objects cause the leaves to repel if charged.

Quantization and Conservation of Charge

• Quantization: Charge is quantized in integral multiples of the elementary charge (e ≈ 1.6 x 10^-19 C).
• Conservation: Total charge in an isolated system remains constant.

Conductors and Insulators

• Conductors: Materials (e.g., metals) with free electrons, allowing easy flow of electric current.
• Insulators: Materials (e.g., rubber) with few free electrons, resisting electric current.

Methods of Charging

• By Friction: Transfer of electrons between two different materials.
• By Conduction: Transfer of charge by contact.
• By Induction: Redistribution of charge in a neutral object due to the presence of a nearby charged object.

Coulomb’s Law

• Describes the electrostatic force between two point charges:
  • Directly proportional to the product of the charges.
  • Inversely proportional to the square of the distance between them.
• Formula: ( F = \frac{k Q_1 Q_2}{r^2} )
  • ( k ) is Coulomb's constant (approximately ( 9 \times 10^9 \text{Nm}^2/\text{C}^2 )).

Electric Field

• Region around a charge where its influence can be felt.
• Electric Field Strength (E): Force per unit positive charge.
• Formula: ( E = \frac{F}{q_0} )
  • Direction: Along the force experienced by a positive test charge.

Electric Field Lines

• Imaginary lines representing the direction of the electric field.
• Properties:
  • Begin on positive charges and end on negative charges.
  • Never intersect.
  • Density of lines indicates field strength.

Electric Field Due to Various Charge Configurations

• Single Charge: Field lines radiate outward for positive and inward for negative charges.
• Dipole: Field lines extend from positive to negative charges.
• Uniform Electric Field: Parallel, equidistant lines.

Superposition Principle

• The net electric field is the vector sum of individual fields due to multiple charges.

Concept of Permittivity

• Free Space Permittivity (( \varepsilon_0 )): A measure of resistance encountered when forming an electric field in a vacuum.
• Influence on Coulomb’s Law: Electrostatic force is inversely proportional to permittivity.

This study guide covers the fundamental concepts related to electric charges and electrostatics, including how charges interact, methods of charging objects, and the principles governing electric fields and forces.