Introduction to Electricity and Magnetism

The following sections are included:

• Dedication
• Preface
• Contents

It is assumed that the reader has had a good course in calculus, is familiar with vectors, and knows Newton’s laws. Apart from that, every effort will be made to keep the presentation of electricity and magnetism self-contained. The goal would be to know and understand the reviews spaced throughout the text. It is assumed that readers will attempt several of the problems from each chapter. It is also assumed that readers will participate in an introductory E&M lab as they go along, in order to obtain some familiarity with the phenomena under discussion.

The following sections are included:

• Electrostatics
• Strength

The following sections are included:

• Superposition
• Examples
  • Point Charge
  • Lines of Force
  • Dipole Field
  • Sheet of Charge
  • Extension
• Electric Flux

From the previous chapter, Gauss’ law is

So far, motivated by our knowledge of mechanics, we have considered forces. We now want to extend the discussion to a consideration of energy.

So far, we have investigated the effects of placing q_test in the vicinity of a collection of fixed charges (Fig. 5.6). Now let us compute the electric energy of the collection of fixed charges themselves.

The following sections are included:

• Capacity
  • Charged Sphere
  • Parallel-Plate Capacitor (“Condenser”)
• Capacitors in Series
• Capacitors in Parallel
• Dielectric
  • Capacity
  • Energy in Capacitor
• Gauss’ Law with Dielectrics

Up until this point, we have dealt with electrostatics. Everything is in equilibrium, and nothing moves. Now we will assume that a potential difference ΔV, and corresponding electric field $\overrightarrow{E}$, have been established somehow, say by a battery, and that the charge flows in the conductor like fluid in a pipe. We now have an electrical current.

The following sections are included:

• Electromotive Force
  • Daniell Cell
  • Lead-Acid Battery
• Simplest Circuit
• Work Done
• Kirchoff’s Rules
  • First Rule
  • Second Rule
• Applications
  • Single-Loop Circuit
  • Multi-Loop Circuit

The following sections are included:

• Coulomb’s Law
• Electric Field
• Gauss’ Law
• Electrostatic Potential
• Electric Energy
• Capacity
  • Dielectric
• Circuits and Ohm’s Law
  • Kirchoff’s Rules

We need to do some math before we launch into magnetism. We first review what we know about vectors.

The following sections are included:

• Magnetism
• The Magnetic Field
  • Analogy to Electrostatics
  • Superposition
  • Gauss’ Law
  • Sources of Magnetic Field
• Biot-Savart Law
  • Line of Current
  • Current Loop
• Lorentz Force

The following sections are included:

• Ampere’s Law
  • Line of Current
  • Current Density
  • Electrostatics and Magnetostatics
• Examples
  • Infinite Current Sheet
  • Two Opposing Sheets
  • Infinite Solonoid
• Lorentz Force (continued)
  • Uniform Circular Motion
  • Electric and Magnetic Fields
  • Velocity Selector
  • Mass Spectrometer
• Force on a Current-Carrying Wire

Suppose we turn the situation around and drive the wire with a velocity $\overrightarrow{v}$ through a uniform field $\overrightarrow{B}$ (Fig. 14.1).

The following sections are included:

• Atomic Magnetism
  • Angular Momentum
  • Spin
  • Quantum Mechanics
• Paramagnetism
• Ampere’s Law with Magnetic Materials
• Ferromagnetism
• Diamagnetism
• Superconductivity

Let us put the circuit elements together and look at time-dependent phenomena. We will just make use of Kirchoff’s second rule in Eq. (10.45), where at any instant the net EMF in the circuit provides a pump that creates a voltage drop across a resistor. The voltage drop across the resistor is then related to the current flowing through it by Ohm’s law.

The following sections are included:

• Vectors
• Magnetic Fields
  • Superposition
  • Gauss’ Law
  • Biot-Savart Law
  • Ampere’s Law
• Lorentz Force
  • Current-Carrying Wire
• Electromagnetic Induction
  • Induced EMF
  • Faraday’s Law
  • Inductance
• Magnetic Materials
  • Atomic Moments
  • Materials
• Time-Dependent Circuits
  • Decaying Currents
  • Oscillators
  • Transformer

The following sections are included:

• The Displacement Current
• Integral Form of Maxwell’s Equations
  • Gauss’ Law for Electric Field
  • Gauss’ Law for Magnetic Field
  • Faraday’s Law
  • Ampere’s Law with Displacement Current
• Time Derivatives
• Gauss’ Theorem
• Stokes’ Theorem
• Differential Form of Maxwell’s Equations

There are many examples of waves in the world around us:

• On strings;
• On membranes;
• On water surfaces;
• In air (sound);
• In solids (sound).

The following sections are included:

• Maxwell’s Equations in Vacuum
• Travelling Wave Solution
• Energy in Wave
• Energy Flux
• Momentum Flux
  • Momentum Density
  • Radiation Pressure
• Amplitude Modulation
• Detection

The following sections are included:

• Standing Waves
  • String with Fixed Endpoints
• Electromagnetic Waves in a Cavity
• Source of Electromagnetic Waves
• Spectrum of Electromagnetic Radiation

The following sections are included:

• Maxwell’s Equations in Vacuum
• Lorentz Transformation
• Einstein’s Theory
• Consequences
  • Velocity of Light
  • Time Dilation
  • Lorentz Contraction
• Transformation Law for Electromagnetic Fields
• Applications
  • Two Moving Charges
  • Electromagnetic Wave
• Basic Principle

The following sections are included:

• Maxwell’s Equations
  • Gauss’ Law
  • Ampere’s Law with Displacement Current
  • Faraday’s Law
  • Maxwell’s Equations
  • Superposition
• Lorentz Force
• Electromagnetic Waves

This section contains the problems on Electricity, Magnetism and Electromagnetism.

The following sections are included:

• Appendix A Significant Names in Electricity and Magnetism
• Appendix B Fundamental Constants
  • B.1 Conversion Factors
• Bibliography
• Index