Essential Calculus-based Physics Study Guide Workbook: Electricity and Magnetism
Book Preface
Prerequisites:
• As this is the second volume of the series, the student should already have studied the material from first-semester physics, including uniform acceleration, vector addition, applications of Newton’s second law, conservation of energy, Hooke’s law, and rotation.
• The student should have learned basic calculus skills, including how to find the derivative of a polynomial or trig function and how to integrate over a polynomial or trig function. This book reviews essential integration skills in Chapter 6.
• The student should know some basic algebra skills, including how to combine like terms, how to isolate an unknown, how to solve the quadratic equation, and how to apply the method of substitution. Needed algebra skills were reviewed in Volume 1.
• The student should have prior exposure to trigonometry. Essential trigonometry skills were reviewed in Volume 1.
Use:
• This book is intended to serve as a supplement for students who are attending physics lectures, reading a physics textbook, or reviewing physics fundamentals.
• The goal is to help students quickly find the most essential material. Concepts:
• Each chapter reviews relevant definitions, concepts, laws, or equations needed to understand how to solve the problems.
• This book does not provide a comprehensive review of every concept from physics, but does cover most physics concepts that are involved in solving problems. Strategies:
• Each chapter describes the problem-solving strategy needed to solve the problems at the end of the chapter.
• This book covers the kinds of fundamental problems which are commonly found in standard physics textbooks.
Help:
• Every chapter includes representative examples with step-by-step solutions and explanations. These examples should serve as a guide to help students solve similar problems at the end of each chapter.
• Each problem includes the main answer(s) on the same page as the question. At the back of the book, you can find hints, intermediate answers, directions to help walk you through the steps of each solution, and explanations regarding common issues that students encounter when solving the problems. It’s very much like having your own physics tutor at the back of the book to help you solve each problem
The goal of this study guide workbook is to provide practice and help carrying out essential problem-solving strategies that are standard in electricity and magnetism. The aim here is not to overwhelm the student with comprehensive coverage of every type of problem, but to focus on the main strategies and techniques with which most physics students struggle.
This workbook is not intended to serve as a substitute for lectures or for a textbook, but is rather intended to serve as a valuable supplement. Each chapter includes a concise review of the essential information, a handy outline of the problem-solving strategies, and examples which show step-by-step how to carry out the procedure. This is not intended to teach the material, but is designed to serve as a time-saving review for students who have already been exposed to the material in class or in a textbook. Students who would like more examples or a more thorough introduction to the material should review their lecture notes or read their textbooks.
Every exercise in this study guide workbook applies the same strategy which is solved step-by-step in at least one example within the chapter. Study the examples and then follow them closely in order to complete the exercises. Many of the exercises are broken down into parts to help guide the student through the exercises. Each exercise tabulates the corresponding answers on the same page. Students can find additional help in the hints section at the back of the book, which provides hints, answers to intermediate steps, directions to walk students through every solution, and explanations regarding issues that students commonly ask about.
Every problem in this book can be solved without the aid of a calculator. You may use a calculator if you wish, though it is a valuable skill to be able to perform basic math without relying on a calculator.
CONTENTS
Introduction 5
Chapter 1 – Coulomb’s Law 7
Chapter 2 – Electric Field 15
Chapter 3 – Superposition of Electric Fields 23
Chapter 4 – Electric Field Mapping 41
Chapter 5 – Electrostatic Equilibrium 55
Chapter 6 – Integration Essentials 65
Chapter 7 – Electric Field Integrals 91
Chapter 8 – Gauss’s Law 113
Chapter 9 – Electric Potential 149
Chapter 10 – Motion of a Charged Particle in a Uniform Electric Field 165
Chapter 11 – Equivalent Capacitance 171
Chapter 12 – Parallel-plate and Other Capacitors 185
Chapter 13 – Equivalent Resistance 195
Chapter 14 – Circuits with Symmetry 209
Chapter 15 – Kirchhoff’s Rules 219
Chapter 16 – More Resistance Equations 231
Chapter 17 – Logarithms and Exponentials 245
Chapter 18 – RC Circuits 251
Chapter 19 – Scalar and Vector Products 259
Chapter 20 – Bar Magnets 265
Chapter 21 – Right-hand Rule for Magnetic Force 269
Chapter 22 – Right-hand Rule for Magnetic Field 279
Chapter 23 – Combining the Two Right-hand Rules 287
Chapter 24 – Magnetic Force 293
Chapter 25 – Magnetic Field 305
Chapter 26 – The Law of Biot-Savart 321
Chapter 27 – Ampère’s Law 345
Chapter 28 – Lenz’s Law 363
Chapter 29 – Faraday’s Law 377
Chapter 30 – Inductance 395
Chapter 31 – AC Circuits 409
Chapter 32 – Maxwell’s Equations 439
Hints, Intermediate Answers, and Explanations 451
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