Introduction to Electricity and Magnetism

Solutions to Problems

John Dirk Walecka

• Publisher: WSPC
• Year: 2019
• eBook ISBN: 9789811202650
• Topic: Physical Sciences
• Subtopic: Electromagnetism

The previously published book Introduction to Electricity and Magnetism provides a clear, calculus-based introduction to a subject that together with classical mechanics, quantum mechanics, and modern physics lies at the heart of today's physics curriculum. The lectures, although relatively concise, take one from Coulomb's law to Maxwell's equations and special relativity in a lucid and logical fashion. That book contains an extensive set of accessible problems that enhances and extends the coverage. As an aid to teaching and learning, the present book provides the solutions to those problems.

Contents:

• Preface
• Electricity:
  • Introduction
  • Coulomb's Law
  • The Electric Field
  • Gauss' Law
  • The Electrostatic Potential
  • Electric Energy
  • Capacitors and Dielectrics
  • Currents and Ohm's Law
  • DC Circuits
  • Review of Electricity
• Magnetism:
  • Vectors
  • The Magnetic Force and Field
  • Ampere's Law
  • Electromagnetic Induction
  • Magnetic Materials
  • Time-Dependent Circuits
  • Review of Magnetism
• Electromagnetism:
  • Maxwell's Equations
  • Waves
  • Electromagnetic Waves
  • More Electromagnetic Waves
  • The Theory of Special Relativity
  • Review of Electromagnetism
• Appendix A: Vector Identities
• Bibliography
• Index

Readership: Undergraduates and academics in physics.Electricity and Magnetism;Electrostatics;Magnetostatics;Electromagnetism;Lorentz Force;Maxwell's Equations;Electromagnetic Waves;Special Relativity0 Key Features:

• Presentation is self-contained even if the text is aimed at the very best students who have completed a good course in calculus and are familiar with vectors and Newton's laws
• Given the astonishing range of applicability of the principles of electromagnetism, the introduction provides a comprehensive foundation to approach many more advanced texts and monographs with a better understanding

PART 1

Electricity

Chapter 1

Introduction

There are no problems associated with the Introduction.

Chapter 2

Coulomb’s Law

Problem 2.1 What is the gravitational force between the two charges in the example in section 2.2? Compare it to the electrostatic force.

Solution to Problem 2.1

The expression for the gravitational force between two masses (m₁, m₂) separated by

is due to Newton

Here

is the force exerted on particle 1 by particle 2, and

is the unit vector

. G is the gravitational constant

We work in SI units where the force is measured in “newtons”

We are asked to compute the magnitude of the gravitational attraction of a completely ionized mole (12 grams) of

separated from San Francisco to New York

The number of atoms in one mole is given by Avogadro’s number

The masses of the carbon nuclei and the electrons (six/atom) are

Hence

This is miniscule compared with the magnitude of the corresponding electrostatic force as calculated in the text

The electrostatic force is as large as it is because of the many-many oppositely charged particles packed into the solid.

Chapter 3

The Electric Field

Problem 3.1 Show that Eq. (3.9) still holds to the given order when the origin of the vector

lies at the midpoint of the displacement

.¹

Solution to Problem 3.1

Suppose the origin of the field vector

lies at the midpoint of the displacement

in the dipole (Fig. 3.1 below). The field is then given by

Fig. 3.1 Origin of the vector

lies at the midpoint of the dipole displacement

.

Write

Then retaining terms up through order d, one has from the binomial theorem in Eq. (3.6)

With the use of this expression

Hence, as requested, we see that the field is still given through order d/r by the result in Eq. (3.9)

Problem 3.2 Make a good numerical calcu...

Table of contents

• Cover
• Title Page
• Copyright Page
• Dedication
• Preface
• Contents
• Part 1 Electricity
• Part 2 Magnetism
• Part 3 Electromagnetism
• Appendix A Vector Identities
• Bibliography
• Index