Study Notes: Chapter 22 – Electric Charges and Forces

Electric Charges and Forces

Introduction to Electric Phenomena

Electric phenomena are fundamental to understanding the behavior of matter and energy. This chapter explores the nature of electric charges, the forces they exert, and the fields they create.

• Electric charge is a property of matter that causes it to experience a force when placed in an electric or magnetic field.

• Electric phenomena are based on charges, forces, and fields.

Types of Electric Charge

There are two types of electric charge: positive and negative. The convention for naming these charges was established by Benjamin Franklin.

• Positive charge: A glass rod rubbed with silk becomes positively charged.

• Negative charge: A plastic rod rubbed with wool becomes negatively charged.

• Objects that repel a charged glass rod are also positively charged; those that attract it are negatively charged.

Charge Model

The charge model explains how objects become charged and interact.

• Charging by friction: Rubbing objects can transfer charge, a process called charging.

• There are only two kinds of charge: "plastic charge" and "glass charge" (historical terms for negative and positive).

• Like charges repel; opposite charges attract.

• The force between charges is a long-range force and increases with the amount of charge and decreases with distance.

• Neutral objects have an equal mixture of both types of charge.

Atomic Structure and Charge Origin

Electric charge originates from the structure of atoms.

• An atom consists of a dense nucleus (containing protons and neutrons) surrounded by orbiting electrons.

• Proton: Mass = $1.67 \times 10^{-27}$ kg, Charge = $+e$

• Electron: Mass = $9.11 \times 10^{-31}$ kg, Charge = $-e$

Particle	Mass (kg)	Charge
Proton	1.67 × 10-27	+e
Electron	9.11 × 10-31	-e

Charge Quantization

Charge is quantized, meaning it exists in discrete amounts.

• The net charge of an object is given by: $q = N_p e - N_e e = (N_p - N_e) e$ where $N_p$ and $N_e$ are the number of protons and electrons, respectively.

• Most objects are neutral ($q = 0$), having equal numbers of protons and electrons.

• A charged object has an unequal number of protons and electrons.

• Charge is always an integer multiple of $e$ (elementary charge).

Ionization and Sharing Electrons

Atoms can gain or lose electrons through ionization.

• Ionization: Removing or adding an electron to an atom.

• Positive ion: Atom loses an electron, net positive charge.

• Negative ion: Atom gains an electron, net negative charge.

Conductors and Insulators

Materials are classified based on their ability to allow charge movement.

• Conductors: Materials (like metals) where charge moves easily. Electrons are loosely bound and can move freely.

• Insulators: Materials (like glass and plastic) where charge does not move easily. Electrons are tightly bound to nuclei.

• Charging by friction leaves immobile patches of charge on insulators.

Polarization and Electric Dipoles

Neutral objects can be polarized by external charges, leading to the formation of electric dipoles.

• Polarization force: A net force toward a charged object due to the redistribution of charges in a neutral object.

• Electric dipole: A neutral atom polarized by an external charge, resulting in separated positive and negative charges.

• Insulators can be modeled as conglomerates of dipoles.

Charging by Induction

Objects can be charged without direct contact through induction.

• Bringing a charged rod near two touching metal spheres polarizes them.

• If the spheres are separated while polarized, they retain net charges of opposite sign.

• This process is called charging by induction.

Coulomb's Law

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

• The magnitude of the force between two charges $q_1$ and $q_2$ separated by distance $r$ is: $F = K \frac{|q_1 q_2|}{r^2}$ where $K = 8.99 \times 10^9$ N·m2/C2 (electrostatic constant).

• Forces are repulsive for like charges and attractive for opposite charges.

• The forces are equal in magnitude and opposite in direction (Newton's third law).

Electric Field Concept

The electric field describes the influence a charge exerts on the space around it.

• Field: A function assigning a vector to every point in space.

• Electric field ($\vec{E}$): The force per unit charge at a point in space.

• For a point charge $q$ at position $(x, y, z)$: $\vec{E}(x, y, z) = \frac{K q}{r^2} \hat{r}$ where $\hat{r}$ is the unit vector pointing from the charge to the field point.

• Units of electric field: N/C (newtons per coulomb).

Unit Vector Notation

Unit vectors are used to specify direction in electric field calculations.

• Unit vector ($\hat{r}$): A vector of length 1 pointing in a specified direction.

• Unit vectors have no units; they only indicate direction.

Practice Problems and Applications

• Calculating the number of excess electrons for a given charge.

• Determining whether a glass bead will "leap up" to a charged plastic sphere using Coulomb's Law and comparing electric force to gravitational force.

• Finding the net force on a charge due to other charges arranged in a rectangle, using vector addition and Coulomb's Law.

Summary Table: Key Concepts

Concept	Description
Charge	Property of matter causing electric force
Conductor	Material allowing free movement of charge
Insulator	Material restricting movement of charge
Coulomb's Law	Force between two point charges
Electric Field	Force per unit charge at a point in space
Polarization	Redistribution of charge in a neutral object
Induction	Charging without direct contact

Example: Calculate the electric field at a distance of 0.053 nm from a proton (as in a hydrogen atom): $E = \frac{K e}{r^2}$ where $e = 1.60 \times 10^{-19}$ C, $r = 0.053 \times 10^{-9}$ m, $K = 8.99 \times 10^9$ N·m2/C2.

Additional info: These notes expand on the original slides by providing definitions, equations, and context for each concept, ensuring a comprehensive and self-contained study guide for exam preparation.