The field of biological physics is a broad, multidisciplinary, and dynamic one, touching on many areas of research in physics, biology, chemistry and medicine. New findings are published in a large number of publications within these disci plines, making it difficult for students and scientists working in biological physics to keep up with advances occurring in disciplines other than their own. The Bi ological Physics Series is intended therefore to be a comprehensive one covering a broad range of topics important to the study of biological physics. Its goal is to provide scientists and engineers with text books, monographs and reference books to address the growing need for information. Books in the Biological Physics Series will emphasize frontier areas of science including molecular, membrane, and mathematical biophysics; photosynthetic en ergy harvesting and conversion; information processing; physical principles of ge netics; sensory communications; automata networks, neural networks, and cellu lar automata. Equally important will be coverage of current and potential applied aspects of biological physics such as biomolecular electronic components and de vices, biosensors, medicine, imaging, physical principles of renewable energy pro duction, and environmental control and engineering. We are fortunate to have a distinguished roster of consulting editors on the Editorial Board, reflecting the breadth of biological physics. We believe that the Biological Physics Series can help advance the knowledge in the field by providing a home for publications in the field and that scientists and practitioners from many disciplines will find much to learn from the upcoming volumes.
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-Hückel 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. Ampère’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) Ampère’s Law.- (iv) Applications of Ampère’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.