1 The Coulomb Force; Electric Field; Electrostatic Potential; Electrostatic Energy.- 1.1 Electric Charge and Coulomb's Law.- 1.1.A. The Electric Structure of Matter.- (i) The Electrostatic Force Between Elementary Charged Particles.- (ii) The Additivity of Electrostatic Forces.- (iii) Are Atoms Electrically Neutral?.- (iv) Quantum Physics and the Size of the Hydrogen Atom.- (v) Mobility of Electric Charges; Conductors and Insulators.- 1.1.B. Definition of the Unit of Electric Charge.- (i) The Electrostatic Unit of Charge.- (ii) The Coulomb and the Flow of Charge.- (iii) Coulomb's Law in the mks System.- (iv) Charge Conservation.- 1.1.C. Summary and Program for the Study of Electrostatics.- 1.2 The Electric Field.- 1.2.A. Test Charges and the Definition of E. The Electric Field Set Up by Some Simple Charge Distributions.- (i) Field of a Single Charge Q.- (ii) Field of Two Charges Separated a Distance from the Origin.- 1.2.B. Field Lines and Their Proper Geometrical Representation.- (i) Construction of Field Lines.- (ii) The Electric Field Distributions for Various Arrangements of Point Charges.- (iii) The Dipole Field.- 1.2.C. Gauss' Law.- (i) The Concept of Electric Flux.- (ii) The Integral Form of Gauss'Law.- (iii) The Differential Form of Gauss' Law.- 1.3 The Electrostatic Potential.- 1.3.A. Coulomb's Law and the Relation Between the Electric Field and the Electrostatic Potential.- 1.3.B. Work Done by a Test Charge. Line Integrals and the Electrostatic Potential.- 1.3.C. Potential of Point Charges, Dipoles, Continuous Charge Distributions, Dipole or Double Layers.- (i) The Potential of a Dipole.- (ii) The Potential Set Up by an Infinite Line of Charge.- (iii) The Potential Set Up by a Double Layer.- 1.3.D. Equipotential Surfaces and Field Lines. Boundary Conditions on the Electrostatic Field and the Potential on Electrical Conductors.- 1.3.E. Laplace's Equation for the Electrostatic Potential in Free Space.- (i) Stockpile of Skeleton Solutions of Laplace's Equation.- (ii) A Metal Sphere in an Initially Uniform Electric Field.- 1.4 Capacitors-Electrostatic Energy Storage.- 1.4.A. The Parallel Plate Capacitor.- (i) Electric Field, Plate Charge, and Capacitance of the Parallel Plate Capacitor.- (ii) Force Between the Plates of a Parallel Plate Capacitor. Electrostatic Field Energy.- 1.4.B. Capacitors of Cylindrical and Spherical Symmetry.- 1.5 The Electrostatics of Nonconductors: Dielectrics and Electric Polarizability.- 1.5.A. Definition of the Dielectric Constant and Electric Susceptibility.- 1.5.B. Induced and Permanent Dipole Moments of Atoms and Molecules. Role of the Boltzmann Factor.- (i) Electronic Polarization of Atoms and Molecules.- (ii) Ionic Polarizability.- (iii) Permanent Electric Dipoles and Their Orientation by an Electric Field.- 1.5.C. Bulk Polarization P. The Relation Between P and the Polarization Surface Charge Density ?pol.- 1.5.D. On the Connection Between the Dielectric Constant ? and the Microscopic Polarizability ?.- 1.5.E. Polarizability of Gases.- (i) Experimental Determination of Induced and Permanent Electric Dipole Moments.- (ii) Classical Model for the Electronic Polarizability of Atoms.- (iii) Permanent Dipole Moments and Their Connection with Molecular Structure.- 1.5.F. The Dielectric Constant of Nonpolar Liquids, Solids, and Liquid Mixtures.- (i) The Local Field and the Clausius-Mossotti Relation.- (ii) Experimental Tests of the Clausius-Mossotti Relation for Dense Gases, Liquids, and Solids.- (iii) Dielectric Constant of Liquid Mixtures.- 1.5.G. Dielectric Constant of Polar Liquids. The Theory of Onsager.- (i) The Failure of the Clausius-Mossotti Formula. The Reaction Field and Spontaneous Polarization.- (ii) The Theory of Onsager for the Dielectric Constant of Polar Media. Comparison with Experimental Data.- 1.5.H. The Electric Field within and Around Dielectric Bodies. Boundary Conditions and the Displacement Vector D.- (i) Laplace's Equation and the Boundary Conditions at the Surface of Dielectric Bodies.- (ii) The Dielectric Sphere in an Initially Uniform Electric Field.- 1.6 Electrostatic Forces and Energy in Dielectric Media.- 1.6.A. Electrostatic Energy, and Forces, for a System of Charges in a Dielectric Fluid.- (i) The Parallel Plate Capacitor.- (ii) The Electrostatic Energy of a Single Charged Sphere.- (iii) The Force Between Two Charges in a Dielectric.- 1.6.B. Water as a Solvent for Ionic Compounds.- (i) The Self-Energy of an Ion in a Dielectric Medium.- (ii) Solubility of Ionic Compounds in Dielectric Solvents.- 1.7 References and Supplementary Reading.- 1.8 Problems.- 2 Electric Currents.- 2.1 Introduction.- 2.2 Current Flow, Electrical Resistance, Ohm's Law, and the Dissipation of Electric Power.- 2.2.A. Flow of Current: Electric Mobility, Conductivity, and Resistivity.- 2.2.B. Ohm's Law.- 2.2.C. Power Dissipation in an Ohmic Conductor.- 2.3 Conductivity of Electrolyte Solutions.- 2.3.A. Theory of the Conductivity of an Electrolyte Solution.- 2.3.B. Comparison Between the Theory and Experimental Measurements of the Mobility and Conductivity.- 2.3.C. Degree of Dissociation of a Weak Acid. With Application to Electrical Conductivity.- 2.4 Electrical Conductivity of Metals.- 2.4.A. Theory for the Electrical Conductivity.- 2.4.B. Comparison with Experimental Data.- 2.5 Electrical Networks with Steady and Time-Varying Current Flow. Kirchhoff's Laws. Resistance, Capacitance, and Operational Amplifier Circuits.- 2.5.A. Circuit Elements; Ideal, Independent Voltage and Current Sources. Kirchhoff's Laws.- (i) Passive Circuit Elements.- (ii) Electrical Networks and Ideal Voltage and Current Sources.- (iii) Voltage and Current Wave Forms.- (iv) Kirchhoff's Laws.- (v) Equivalent Voltage and Current Sources.- (vi) Voltage, Current, and Power Transfer.- 2.5.B. Transducers and Simple Resistive Networks Used for Measurement and Control.- (i) Transducers for the Measurement of Temperature, Pressure, and Strain.- (ii) The Wheatstone Bridge for the Measurement of Electrical Resistance.- (iii) The Potentiometer for the Measurement of Voltage.- 2.5.C. Time-Varying Current Flow in Circuits Containing Resistors and Capacitors.- (i) The Series Resistance-Capacitance (RC) Circuit.- (ii) The Elements of Alternating Current Circuit Theory.- 2.5.D. Operational Amplifiers.- (i) Basic Properties of an Ideal Operational Amplifier.- (ii) Departure of Actual Op-Amps from Ideality.- (iii) Linear Operational Amplifier Circuits Using Feedback.- 2.6 The Electrical Determination of the Capacitance and the Thickness of the Cell Membrane.- 2.6.A. The Electrostatic Capacitance and the Energy Stored in the Cell Membrane.- 2.6.B. Method of Measurement of the Cell Membrane Capacitance: Connection with Alternating Circuit Theory.- 2.7 Charge and Current Flow in Three Dimensions: The Continuity Equation and Charge Neutrality: Quasi-Stationary Flow. Application to Lightning Bolts and Current Flow in the Earth.- 2.7.A. The Continuity Equation and Charge Neutrality in a Conducting Medium.- 2.7.B. Quasi-Stationary Current Flow.- 2.7.C. Lightning Bolts and Current Flow in the Earth.- 2.8 Electrocardiography.- 2.8.A. Elementary Anatomy and Electrophysiology of Heart Nerve and Muscle Cells. Double Layers; and Transcellular Potential Differences.- 2.8.B. Depolarization of the Heart. The Heart Vector P(t).- 2.8.C. Electrical Activity of the Heart. P (t) for the Normal Heart.- 2.8.D. Electric Potential Lines on the Body Surface. The Spherical Model.- 2.8.E. Scalar and Vector Electrocardiography.- 2.9 References and Supplementary Reading.- 2.10 Problems.- 3 Electrochemistry and Bioelectricity.- 3.1 The Diffusion of Ions and the Nernst-Planck Equation.- 3.1.A. Ion Flow Due to Diffusion and Electric Fields. The Nernst-Planck Electrodiffusion Equation.- 3.1.B. Diffusion Potentials, Liquid Junctions, and Salt Bridges.- (i) Diffusion Potential in a Single Electrolyte of Nonuniform Concentration.- (ii) Junction Potential Across the Boundary of Two Distinct Electrolytes.- (iii) Salt Bridges; Measurement of Cell Membrane Potentials.- 3.1.C. Debye Shielding: The Ion Cloud Around an Electrically Charged Surface.- (i) The Equilibrium Ion Concentrations and Equilibrium Electrostatic Potential. The Boltzmann Factor.- (ii) The Poisson-Boltzmann Equation. Debye Length Defined.- (iii) Solution of the Linearized Poisson-Boltzmann Equation.- (iv) Magnitude of the Debye Shielding Distance. The Ionic Strength of a Solution.- (v) Can the Debye Length Be Measured?.- (vi) Debye Shielding of a Charged Sphere.- 3.1.D. Electrophoresis.- (i) Some Observations on Protein Structure and Electric Charge.- (ii) The Electrophoretic Mobility of a Charged Particle.- (iii) Electrophoretic Measurements.- 3.2 Galvanic Cells; Electrodes; Electrochemical Measurements; pH Determination.- 3.2.A. Introduction-Galvanic Cells.- (i) Electrode Reactions. Anode and Cathode Defined.- (ii) Resting Potential of a Galvanic Cell as the Sum of Electrode Potentials, Contact Potentials, and Junction Potentials.- (iii) Reversible Electrode Processes.- (iv) Electrodes of the Second Kind.- (v) The Hydrogen Electrode.- 3.2.B. The Electromotive Force of a Galvanic Cell.- (i) The Nernst Equation for Half-Cell Potentials.- (ii) Experimental Test of the Nernst Relation.- (iii) Concentration, Activity, and Activity Coefficients.- (iv) Debye-Huckel Theory of Activity Coefficients.- 3.2.C. Electrochemical Measurements: The Ionic Product of Water. pH Measurements; Acid Equilibrium Constants.- (i) The Ionic Product of Water.- (ii) pH Determination.- (iii) Equilibrium Constants of Weak Acids.- (iv) The Glass Electrode.- 3.3 Membrane Potentials. Biomembranes. Active Transport of Ions. Excitable Membranes and the Action Potential.- 3.3.A. Introduction to Bioelectric Phenomena.- (i) A Short Historical Introduction.- (ii) Biomembranes; The Physiological Role of Membrane Potentials.- 3.3.B. Membrane Potentials.- (i) The Donnan Equilibrium.- (ii) Electrolyte Composition of Intracellular and Extracellular Fluids, and Observed Membrane Potentials.- (iii) The Ussing Flux Ratio Criterion, and the Sodium Pump.- (iv) Current-Voltage Relations for a Biomembrane.- 3.3.C. Excitable Membranes; Axons and the Action Potential.- (i) The Axon as a Cable.- (ii) The Action Potential and Associated Transmembrane Currents.- (iii) A Sketch of the Work of Hodgkin and Huxley.- (iv) The Existence of a Firing Threshold.- 3.4 References and Supplementary Reading.- 3.5 Problems.- 4 Electromagnetism.- 4.1 The Magnetic Field and Magnetic Force.- 4.1.A. Introduction: Elementary Magnetic Phenomena.- 4.1.B. The Lorentz Force.- (i) Force on a Moving Isolated Charge and the Definition of the Magnetic Field B.- (ii) Magnetic Force on a Differential Element of Current.- (iii) Torque on a Current Loop. The Magnetic Dipole Moment.- (iv) Energy of Interaction Between a Magnetic Dipole and a Magnetic Field.- 4.1.C. The Magnetic Field Produced by Differential Current Elements. The Law of Biot and Savart. Ampere's Law.- (i) The Magnetic Field of a Straight Line of Current.- (ii) The Magnetic Field of a Small Current Loop. The Magnetic Dipole Field.- (iii) Ampere's Law.- (iv) Applications of Ampere's Law: Field Inside a Thick Wire, and the Field Inside a Long Solenoid.- 4.2 Faraday's Law of Induction.- 4.2.A. Magnetic Flux and Induced Electromotive Force.- (i) Basic Observational Facts Underlying Faraday's Law.- (ii) Definition of Induced Electromotive Force and Magnetic Flux. Statement of Faraday's Law and Lenz's Rule.- 4.2.B. Self-Inductance, Mutual Inductance, Electrical Circuits with Inductance. Electrical Resonance.- (i) Definition of Self-Inductance.- (ii) The Inductor as a Circuit Element. The Simple R-L Circuit.- (iii) The Series R-L Circuit Driven by an Alternating Voltage Source.- (iv) Circuits Containing Resistance, Capacitance, and Inductance. Electric Resonance.- (v) Mutual Inductance of Two Current Loops.- (vi) The Transformer as a Circuit Element.- 4.3 Maxwell's Equations and Electromagnetic Waves.- 4.3.A. Summing Up: Statement of Maxwell's Equations.- (i) The Field Concept.- (ii) Charge, Current, and Charge Conservation.- (iii) Properties of the Electric Field.- (iv) Properties of the Magnetic Field.- 4.3.B. Electromagnetic Waves.- (i) Waves and the Wave Equation.- (ii) Electromagnetic Plane Waves.- (iii) Sinusoidal Waves. Linear and Circular Polarization.- (iv) The Electromagnetic Spectrum.- 4.4 References and Supplementary Reading.- 4.5 Problems.- Table of Basic Constants.- Table of MKSA Units.
