Chapter One: Electric Charges and Fields

1.1 Introduction

• Everyday experiences of electric discharge: sparks, crackles, and shocks.
• Static electricity arises from electrostatics, which deals with forces, fields, and potentials from static charges.

1.2 Electric Charge

• Discovery by Thales of Miletus: Amber attracts light objects when rubbed with wool.
• Electricity derives from "elektron" (Greek for amber).
• Electric charge types: positive and negative (like charges repel, unlike charges attract).
• Charges are neutralized upon contact. Benjamin Franklin named charges positive (glass) and negative (plastic).
• Detection: Gold-leaf electroscope shows charge by leaf divergence.
• Electrification: Addition or removal of electrons.

1.3 Conductors and Insulators

• Conductors allow electricity flow; insulators do not.
• Semiconductors have intermediate resistance.
• Conductors: metals, human/animal bodies, earth.
• Insulators: glass, plastic, nylon.

1.4 Basic Properties of Electric Charge

1.4.1 Additivity of Charges

• Total charge is the algebraic sum of individual charges.

1.4.2 Charge is Conserved

• No creation/destruction, only transfer of charge.

1.4.3 Quantisation of Charge

• Charge is quantized in multiples of the elementary charge (e).

1.5 Coulomb's Law

• Force between two point charges is proportional to their product and inversely proportional to the square of their separation.
• Law discovered using a torsion balance.
• Inverse square law holds in electrostatics and gravity.

1.6 Forces Between Multiple Charges

• Superposition principle: Force on a charge is the vector sum of individual forces from other charges.

1.7 Electric Field

• Electric field (E) represents force on a unit positive charge.
• Field due to a charge is radially outward (positive) or inward (negative).
• Electric field expressions involve superposition for multiple charges.

1.8 Electric Field Lines

• Field lines represent electric field direction and strength.
• Properties: start at positive and end at negative charges, never cross, and don't form closed loops.

1.9 Electric Flux

• Flux quantifies the electric field passing through a surface (E·dS).
• Orientation affects flux calculation.

1.10 Electric Dipole

• Consists of equal and opposite charges separated by a distance.
• Characterized by dipole moment (p = q * 2a).
• Field of a dipole decreases faster than a single charge.*

1.11 Dipole in a Uniform External Field

• Dipoles align with external fields due to torque (τ = p × E).
• In non-uniform fields, dipoles experience net force.

1.12 Continuous Charge Distribution

• Charge distribution can be linear, surface, or volume.
• Electric field calculated by integrating over distribution.

1.13 Gauss’s Law

• Electric flux through a closed surface equals the enclosed charge divided by permittivity.
• Useful for symmetrical charge distributions.

1.14 Applications of Gauss’s Law

• Calculating fields for symmetrical distributions: long wire, plane sheet, spherical shell.

Summary

• Key concepts: types of charge, quantization, conservation.
• Coulomb's law and superposition principles.
• Electric field and potential concepts.
• Importance of Gauss's Law in practical applications.