Electric Charge and Electric Field: Fundamental Concepts and Laws

Chapter 21: Electric Charge and Electric Field

Experiments in Electrostatics

Early experiments with amber and cloth revealed the attractive properties of electrified materials, laying the foundation for the study of electrostatics. These observations led to the identification of electric charge and its behavior.

• Thales of Miletus (600 BC): Observed that amber, when rubbed, attracted light objects.

• William Gilbert (1600): Coined the term "electricity" from the Greek word for amber, electron.

• Benjamin Franklin (1747): Established the convention of positive and negative charges, associating glass rods with positive and plastic (amber, rubber) rods with negative.

Goals for Chapter 21

• Study electric charge and charge conservation

• Understand how objects become charged

• Calculate electric force using Coulomb's law

• Distinguish between electric force and electric field

• Calculate electric fields due to multiple charges

• Visualize and interpret electric fields

• Calculate properties of electric dipoles

First Observations – Greeks

Ancient Greeks observed both electric and magnetic phenomena. Amber, when rubbed, became electrified and attracted small objects. Magnetite was found to attract iron, revealing magnetic forces.

Properties of Electric Charges

Electric charge is a fundamental property of matter, existing in two types: positive and negative.

• Like charges repel, unlike charges attract.

• Proton: Carrier of positive charge, immobile within the nucleus.

• Electron: Carrier of negative charge, mobile and responsible for charge transfer.

• Charge Conservation: Charge is neither created nor destroyed, only transferred.

• Charge Quantization: All charge is a multiple of the elementary charge, $e = 1.6 imes 10^{-19}$ C.

Characteristics of Particles

Particle	Charge (C)	Mass (kg)
Electron	-1.60 × 10-19	9.11 × 10-31
Proton	+1.60 × 10-19	1.67 × 10-27
Neutron	0	1.67 × 10-27

Conductors, Insulators, and Semiconductors

• Conductors: Materials (e.g., copper, aluminum, silver) where charges move freely. Charge distributes over the surface.

• Insulators: Materials (e.g., glass, rubber) where charges do not move freely. Charge remains localized.

• Semiconductors: Intermediate properties (e.g., silicon, germanium).

Charging Mechanisms

Charging by Conduction

Occurs when a charged object contacts another, transferring electrons. The object being charged acquires the same sign as the charging object.

Charging by Induction

Occurs without direct contact. A charged object brought near a conductor causes redistribution of charges, and grounding allows electrons to move, leaving the object with induced charge.

Polarization

In neutral atoms/molecules, centers of positive and negative charge coincide. A nearby charged object can separate these centers, causing polarization, which explains phenomena like a charged comb attracting paper.

Experiments Verifying Charge Properties

• Faraday's Ice-Pail Experiment: Demonstrated charge rearrangement in conductors.

• Millikan Oil-Drop Experiment: Measured the elementary charge and confirmed charge quantization ($q = n e$).

Coulomb's Law

Coulomb's Law quantifies the force between two point charges:

• Force is along the line joining the charges.

• Force is inversely proportional to the square of the separation distance.

• Force is proportional to the product of the magnitudes of the charges.

• Attractive for opposite signs, repulsive for like signs.

Mathematical Form:

$F = k_e rac{|q_1 q_2|}{r^2}$

where $k_e = 8.99 imes 10^9$ N m2/C2

Vector Nature of Electric Forces

Electric force is a vector quantity. For two charges, the force on each is equal in magnitude and opposite in direction. The principle applies to both repulsive and attractive interactions.

Superposition Principle

When multiple charges are present, the net force on any charge is the vector sum of the forces from all other charges:

• Add forces as vectors.

• Use diagrams and resolve components for calculation.

Problem Solving Strategy

1. Draw a diagram of the charges.

2. Identify the charge of interest.

3. Convert all units to SI.

4. Apply Coulomb's Law for each pair.

5. Sum all x- and y-components.

6. Find the resultant force using the Pythagorean theorem and trigonometry.

Additional info:

• These notes cover the foundational concepts of electric charge, types of materials, charging mechanisms, and the laws governing electric forces, suitable for introductory college physics.