Electric Charge and Electric Fields

Introduction

This section introduces the fundamental concepts of electric charge and electric fields, which are foundational to understanding classical electromagnetism. The material covers how objects become electrically charged, the conservation of electric charge, and the calculation of electric forces using Coulomb's law.

Relationship to Maxwell’s Equations

Maxwell’s Equations are the cornerstone of classical electromagnetism (E&M), describing how electric and magnetic fields are generated and altered by charges and currents. In this chapter, the focus is on static situations involving electric charges and electric fields.

• Gauss’s Law for Electricity: Where is the electric field, is the charge density, and is the vacuum permittivity constant.

• Other Maxwell’s Equations: (for reference)

Additional info: In electrostatics, only Gauss’s Law is directly relevant, as magnetic and time-varying effects are not present.

Electric Charge

Nature of Electric Charge

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electric or magnetic field. The study of stationary charges is called electrostatics.

• Charging by Friction: Rubbing certain materials (e.g., plastic rods with fur, or glass rods with silk) can transfer charge, causing the objects to become electrically charged.

• Like Charges Repel, Unlike Charges Attract: Two plastic rods rubbed with fur repel each other; two glass rods rubbed with silk also repel. However, a plastic rod rubbed with fur and a glass rod rubbed with silk attract each other.

• Types of Charge: There are exactly two kinds of electric charge:

  • Negative charge: The type acquired by plastic rods rubbed with fur.

  • Positive charge: The type acquired by glass rods rubbed with silk.

Definition: Electrostatics is the study of electric charges at rest.

Structure of Matter and Charge

Atoms are composed of three types of subatomic particles:

• Electrons: Negatively charged, mass kg, charge C.

• Protons: Positively charged, mass kg, charge C.

• Neutrons: Electrically neutral, mass kg.

The nucleus contains protons and neutrons, while electrons form a cloud around the nucleus.

Atoms, Ions, and Charge Conservation

• Neutral Atom: Equal number of protons and electrons; net charge is zero.

• Positive Ion (Cation): Atom with one or more electrons removed; net positive charge.

• Negative Ion (Anion): Atom with one or more extra electrons; net negative charge.

• Charge Quantization: All observable charge is an integer multiple of the elementary charge .

• Conservation of Charge: The total electric charge in a closed system remains constant.

Example: The total positive charge in one mole of sodium atoms (with 11 protons per atom) can be calculated using Avogadro’s number ().

Conductors and Insulators

Definitions and Properties

• Conductors: Materials (e.g., metals like copper) in which electric charge can move freely.

• Insulators: Materials (e.g., nylon, glass) in which electric charge does not move freely.

Example: A metal ball connected to a charged plastic rod via a copper wire becomes charged, demonstrating conduction. Nylon thread, being an insulator, does not allow charge transfer.

Charging by Induction

Charging by induction is a process by which a conductor can be charged without direct contact with a charged object.

1. Bring a charged rod near (but not touching) a neutral metal object; free electrons in the metal redistribute due to electrostatic repulsion or attraction.

2. Connect the far side of the metal object to the ground with a wire; electrons flow to or from the ground.

3. Remove the ground connection, then remove the charged rod. The metal object is left with a net charge opposite to that of the rod.

Electric Forces on Uncharged Objects

Polarization and Attraction

• Polarization: A charged object can induce a redistribution of charge within a neutral insulator, causing one side to become slightly positive and the other slightly negative.

• Attraction: Both positively and negatively charged objects can attract neutral insulators due to polarization effects.

Example: A charged comb can pick up small pieces of paper, even though the paper is neutral.

Applications: Electrostatic Painting

• Negatively charged paint droplets are attracted to a positively charged or grounded metal object, improving paint coverage and reducing waste.

Measuring the Electric Force: Coulomb’s Law

Coulomb’s Law

Coulomb’s law quantifies the electric force between two point charges:

• The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Formula:

• = magnitude of the force between charges

• = charges

• = distance between charges

• N·m2/C2 (Coulomb’s constant)

Principle of Superposition

• If multiple point charges are present, the net force on any one charge is the vector sum of the forces exerted by all other charges.

• This property is called superposition and is fundamental to all field theories in physics.

Comparison: Electric vs. Gravitational Force

• Both forces are inverse-square laws, but the electric force is much stronger than the gravitational force for elementary particles.

• Gravitational Force: , where is the gravitational constant.

• Electric Force:

Example: The electric force between two electrons is vastly greater than the gravitational force between them.

Vector Addition of Electric Forces

• When more than two charges are present, calculate the force from each charge separately and add the vectors to find the net force.

• Use trigonometry and vector components for charges not aligned along a straight line.

Example: Three charges placed along a line: calculate the net force on the central charge by summing the forces from the other two.

Summary Table: Comparison of Electric and Gravitational Forces

Additional info: Quantum mechanics is required for a full understanding of charge quantization and the behavior of electrons in atoms, but classical electrostatics provides an accurate description for most macroscopic phenomena.