Charges and currents

Type of physical science: Classical physics

Field of study: Electromagnetism

Given the enormous use and importance of electric and electronic devices in daily life, a clear understanding is needed of the nature of charges and currents, what effects they produce, and how to control those effects.

Overview

Charge is a fundamental concept needed in physics to understand the nature and effects of electric and magnetic fields. It cannot be expressed in terms of the other three fundamental physical concepts: mass, length, and time. It came to be understood through experimental study.

Take, for example, two pieces of glass and two pieces of amber. If one piece of glass and one piece of amber are rubbed together and separated, it is noticed that the rubbed surfaces have a tendency to attract each other. Now, if the other piece of glass is rubbed with the second piece of amber and the rubbed surface of glass is brought close to the first piece of glass, they repel. Similar repulsion also takes place between the two amber pieces. In this experiment, the rubbed surfaces are charged surfaces, and the observed attraction and repulsion phenomena are called electrical phenomena. The experiment shows that there are two types of charges, and one of these is called positive and the other, negative. The experiment also demonstrates that like charges repel and unlike charges attract.

Charging is accomplished through friction. Also, metals can be charged by induction.

For example, if a hollow metallic vessel is hung by silk threads and the charged amber from the first experiment is suspended anywhere inside the vessel but without touching the metallic vessel, the outside of the vessel becomes positively charged. If the charged amber is removed, the charge on the vessel is gone, too. If there is a second metallic vessel, which is connected to the first metallic vessel with a metallic wire, the second vessel also becomes positively charged.

This charge also disappears when the original charged amber hanging in the first vessel is removed. Somehow, the charge on the first vessel is transferred to the second through the metallic wire. On the other hand, if a glass rod had been used instead of a metallic wire to connect the two metallic vessels, no charge on the second vessel would have been observed. The second experiment indicates that some substances can conduct electricity and some cannot.

Materials such as metals, which can conduct electricity, are called conductors, and materials such as glass, which cannot conduct electricity, are called insulators.

Some of these concepts were well understood in the nineteenth century. In the 1800's, serious efforts were under way to understand the physical laws governing the behavior of charges and to develop mathematical formulations for those laws. The first important law of effects of charges on one another was formulated by Charles-Augustin de Coulomb. The law states that the force of repulsion between the two-point charges is along the line joining the charges. It is proportional to the product of the magnitudes of the charges and inversely proportional to the distance between them. The constant of proportionality is chosen as 1.1/10²⁴.

When there are several charges, all their effects can be found by adding the effective forces due to each one of them vectorially. Later, the basic measuring unit for charges was chosen as coulomb. Coulomb is the charge that, when it is a distance of 1 meter from an equal amount of like charge, is repulsed with a force of 1 newton. Another law, discovered by Benjamin Franklin, is that charge is conserved in any given experiment.

The third law was developed after the structure of the atom was discovered. It is known now that all atoms have negatively charged particles called electrons, moving in orbits around a nucleus that is a central core of positive and uncharged particles. Robert Andrews Millikan measured the charge of an electron to be 1.6 x 10^-19 coulombs. It was found experimentally that all electrical charges could exist only in positive or negative multiples of the magnitude of the charge of an electron. Thus, it can be said that charge is quantized.

Charges can be transferred from one body to another: Consider two concentric spherical conductors. The inner conductor has charge that resides on its outer surface. If the outer sphere is isolated, then its inner surface will have an equal amount of negative charge, and its outer surface will have the same amount of positive charge. The outer surface is now connected to ground, the charge on it is removed, and the ground is disconnected. If the inner sphere is removed, the negative charge on the inner surface of the outer sphere can be transferred to a third body. This process can be repeated several times for transferring charges.

Charge can be discrete or continuous in space. The electronic nature of charges, however, indicates that all charges are ultimately discrete in nature. Depending on whether charges are distributed along a wire, on a surface, or in a volume, the concepts of charge per unit length (linear charge density), per unit area, or per unit volume are defined. Such definitions are extremely useful in developing mathematical formulations. Charges can be stationary or moving.

They can have varying magnitude in time. Stationary charges produce electric fields that are constant in time. Fluctuating and moving charges have other important properties.

A recommended method to study the effects of discrete charges is to analyze the effects of dipole and multipole. A multipole has several discrete charges at fixed separations. A dipole consists of two equal and opposite charges at some fixed separation. Even though its charge is neutral, it produces external effects. It is a concept that has many applications in the study of the behavior of dielectrics, laser physics, intermolecular forces, and polarization. Continuous charges are studied using the sophisticated mathematical techniques from calculus and related analysis.

A moving charge constitutes current. Current is defined as the time rate of flow of charge. Currents are generated in a variety of ways. If two different materials--for example, lead and lead oxide dipped in a sulfuric acid--are connected with metallic wire, it is observed that a current flows in them. When a piezoelectric crystal, such as ammonium dihydrogen phosphate, is strained between two metallic contacts, current flows in the metallic wire connecting the contacts. If some materials such as tungsten coil are heated to high temperatures, they emit electrons, which constitute a flow of current. Light falling on some materials such as gallium arsenide can also generate current. Most often, metals are used for carrying current, since electrons in metals can move freely from place to place. For example, if terminals of a battery with some voltage are connected with metallic wires, charges drift along the wires and constitute conduction current. There are other materials, such as mica and rubber, that cannot conduct current; these are called insulators. Much of modern electronics depends on semiconductors, which can carry current reasonably but not as well as metals. The basic unit for measuring current is the ampere, which is a transfer of charge of one coulomb per second at a given point.

Depending on whether charges are moving across a surface or a volume, surface current density or volume current density is defined. Such definitions will be useful in the mathematical formulations of physical laws that govern the behavior and effects of currents.

Currents can be static or fluctuating. A static current, also called a direct current, is a flow of charge in which current does not change its magnitude in time or direction. When magnitude of current varies as a sinusoidal function of time, it is called alternating current. The study of currents in electronics is divided into two branches: one for alternating current and another for direct current. This division results from the fact that principles of transport and some effects of alternating currents are drastically different from those of direct currents. There are also other important fluctuating currents, such as current pulses, where current keeps changing its magnitude in time alternately from zero to a constant value and back to zero.

Unlike direct current, alternating current can flow even if there is no direct metallic contact between two points. It was found experimentally that if two terminals of a generator are connected with fluctuating voltage and two separate wires to two separated, parallel metallic plates, current will flow in the wires. Thus, the charge is transported across the plates, even though the plates are not touching each other. This charge transfer per unit time is called displacement current. The concept of displacement current was first introduced by James Clerk Maxwell. Displacement current contrasts with current flow along the metallic wires, which is called conduction current. Also, the separated parallel plates, across which the alternating currents but not the direct currents can flow, constitute what is called a capacitor. This transport of current is caused by the fact that effects such as forces that result from charges are felt at distances far beyond the dimensions of charges.

All types of currents produce magnetic fields. This effect is one of the most important discoveries in physics because for several centuries, scientists thought that magnetism and electricity were two different phenomena. Static current produces magnetic fields that do not change in time. Andre-Marie Ampere showed that two parallel wires attract each other if the currents flow in opposite directions and repel each other if the currents flow in the same direction. It has been established experimentally that the magnetic field produced by a current element moves in a direction perpendicular to the direction of the current flow and to the line joining the point of observation of the magnetic field and the current element. The magnitude of the magnetic field is proportional to the magnitude of current and inversely proportional to the distance between the point of observation and the current element.

Another important property is current continuity. When a steady current flows across a wire, its magnitude must be the same all along the wire; otherwise, charge accumulation takes place somewhere in the wire, which is not possible. This property is called current continuity. It appears that this law would be violated for alternating currents. Yet, taking into consideration displacement current, this law can be shown to hold firm.

Another interesting effect was found by Michael Faraday. He discovered that a fluctuating magnetic field in the vicinity of a closed metallic coil generates current in the coil, which tends to oppose the applied magnetic field. This effect means that the behavior of a metallic coil for alternating currents differs from that for direct currents and for alternating currents; the metallic coil is said to constitute inductors. By having two coils side-by-side, it is therefore possible to transfer current from one coil to another coil; the two coils together are called transformers. This effect is not observed for direct currents. Finally, it is found that fluctuating electric currents radiate. A changing current in a closed path produces a changing magnetic field; this changing magnetic field will result in a changing electric field, which alters the displacement current. The changing displacement current leads to further changes in the magnetic field; as a result, electric and magnetic fields will move away from the circuit, which produces electromagnetic wave radiation.

There are several other important laws and phenomena associated with charges and currents. For example, one may want to know about the speed with which current flows in a given substance; the resistance of the substance to the flow; the transformation of current into other forms of energy, such as heat and light; and how these issues are related to the physical and chemical properties of the substance itself. Such laws are understood through a thorough study of solid-state physics. These and other questions led to the development of principles of modern-day electrical and electronics engineering.

Applications

Many important applications of electricity in day-to-day life depend on the conversion of electrical energy into other forms of energy, such as mechanical work, light, and heat. Many of these applications were conceived in the nineteenth century and were subsequently refined. In the twentieth century, an understanding of the atomic electronic nature of charges and currents led to the birth of electronic devices such as radio and television.

A battery is a device that converts chemical energy into electrical energy by transferring electrons from one material to another material. For example, in a lead acid battery, a sponge lead is used as the negative electrode, lead oxide as the positive electrode, and a sulfuric acid solution as the electrolyte. Electrons are transferred through the electrolyte from the positive electrode to the negative electrode, thereby developing charged electrodes with an electromotive force between them. Despite having only a crude understanding of electric charges, electrodes, and electrolytes, Alessandro Volta built a battery cell in 1820. Later, the Daniel cell and other battery cells were invented. These chemical batteries are used in automobiles, watches, calculators, radios, and flashlights.

Electric lamps are built by using one of essentially two methods to convert electrical energy into light. First, current flow in some materials generates heat, which, when the materials are heated to high enough temperatures, causes these materials to glow. This fact was known for quite some time, and tempted several researchers to develop carbon arc lamps, which worked, but not very well. Thomas Alva Edison and Joseph Wilson Swan developed incandescent carbon filament lamps, which were much more reliable and successful and led to the development of electric lights through tungsten filament lamps. The second method to build electric lamps is to use electric discharge. Here, a sealed tube is used, with two electrodes at each end. The inner surface of the tube containing low-pressure mercury vapor and inert gas mixture is coated with phosphor. When suitable voltage is applied, fluorescence of phosphor will lead to bright light.

After it was discovered that a metallic coil moving in a magnetic field could generate current, large magnets and coils were used to produce electric power for lighting and heating houses and street lamps. These coils were rotated by using energy from other sources, such as mechanical energy from a body of freely falling water, which generated an alternating current.

Later, rectifiers were developed to convert alternating current into direct current. Later advances in electrical technology led to the modern sophistication of generation and control of electric power.

According to Ampere's law, the wires carrying currents may attract or repel. Faraday's law states that a magnetic field can induce currents in moving conductors. Through the use of these laws, efforts were made to convert electrical energy into mechanical energy, which led to the development of small electric motors for household use. The first electrical motor was invented by Thomas Davenport. The rapid progress of electrical technology required the development of measuring instruments, such as ammeters, voltmeters, and galvanometers.

An understanding of atomic structure and charge conservation in a chemical reaction led to the rapid development of the concept of valency. By discovering how many electrons are needed to fill the outermost orbit of several atoms completely, one can determine which elements can be combined to form compounds. The concept of valency provided a solid foundation for physical chemistry.

Charges can be released from several materials by subjecting them to heat, strong electrical fields, and electromagnetic radiation. These charges and resulting currents can be controlled using electric and magnetic fields, a concept that resulted in the development of modern electronics. The triode that gave birth to radio engineering consisted of a vacuum tube with a tungsten filament, which released electrons when current was passed through it, and a metallic plate that collected these electrons when it had a suitable polarity; a metallic grid was placed between the filament and the plate. It was found that a small weak electrical alternating voltage applied between the grid and the filament generated an amplified voltage between the plate and cathode tube. In the 1950's, it was discovered that this amplification could be achieved within materials such as silicon and germanium. In addition, several techniques were invented to control the flow of charge carriers. These inventions led to transistors and integrated circuits which, in turn, led to the explosive development of modern-day radio, television, and communications technologies.

Context

Historically, ancient Greeks knew that some materials could be charged by friction.

Also, the magnetic properties of lodestone, a natural magnet, were known. The connection between these apparently separate phenomena came much later. In 1600, William Gilbert wrote a book containing a detailed study of magnetism and electrification by friction. Gilbert postulated that electrification was caused by the removal of a fluid (charge) by friction, which then created an atmosphere (field). Franklin introduced the concept of positive and negative charges and announced the law of conservation of charge. Coulomb and Simeon-Denis Poisson were responsible for the mathematical formulation of several laws of electrostatics, including the inverse law of attraction and repulsion between charges.

In 1791, Luigi Galvani, a professor of anatomy in Bologna, found that when a frog's muscle and nerve were connected through a metallic wire, some muscular contraction was observed, indicating there was some current flow in the wire. Volta, following Galvani's research, developed the voltaic cell (electrochemical battery) in 1792. In 1820, Hans Christian Ørsted discovered that currents produce magnetic fields. Ampere discovered the conditions under which two current-carrying wires attract or repel. The laws developed by Ørsted and Ampere were put in a mathematical form by Jean-Baptiste Biot and Felix Savart.

The ability of materials to let current flow through them was studied by Georg Simon Ohm in 1827. Later, James Prescott Joule found that current flow in some conductors could produce heat. This discovery created an interest in determining the relationship of electric energy and magnetic energy to other forms of energy. Several scientists, especially Joseph Henry and Lord Kelvin, studied the effects of propagation of current through conductors. Even today, this area is one of the most actively pursued research topics. Faraday discovered the law of electromagnetic induction in 1831 and introduced the concept of lines of force to facilitate the study of electrostatics. Heinrich Friedrich Emil Lenz discovered the laws relating the directions of induced current and the magnetic field that causes it.

A study of the experimental works of all these scientists led to efforts by others to develop a theory unifying electricity, magnetism, and optics. This research was given further impetus after it was discovered that the ratio of electric and magnetic units is the same as the velocity of light in dimensions and magnitude. A general theory for electromagnetism and optics was developed by Maxwell.

On the chemistry side, the work on discharge of rarefied gases, which was originally researched by Faraday, was pursued by Sir John Joseph Thomson and Sir John Sealy Edward Townsend, who found that the rays emitted from cathode in a discharge tube were only streams of negatively charged particles, lighter than all atoms known. These particles, named electrons, constitute one of the fundamental particles of all matter; later, Millikan measured the charges of an electron. Francis William Aston discovered the positive charge carrying fundamental particles of matter in all atoms and called it a proton.

Efforts to explain various phenomena in physics, especially those in nuclear physics, and a desire to develop a unified field theory led to the postulation of various charged and uncharged subatomic particles. In all cases, however, the charges of the subatomic particles were always found to be an integral multiple of the charge of the electron. The reasons for this mathematical relationship were not clear. In the 1960's, it had become necessary to introduce particles carrying charges of magnitude less than that of the electron. Called quarks, their existence was proved experimentally. Also, it is not clear why the electron charge remains the same for all matter. Continued research of subatomic particles and their interaction may lead to a better understanding of charges and any previously unobserved effects, which could result in a better understanding of matter, and thereby lead to new technologies. Examining the biological effects of electromagnetic radiation is another area of research that is challenging scientists.

Current flow through semiconductors and several newly synthesized materials continues to be a very important research topic, which may lead to further advances in electronics.

Principal terms

ALTERNATING CURRENT: a current whose magnitude varies as a sinusoidal function of time; characterized by its frequency, measured in hertz, and magnitude, measured in amperes; one ampere is one coulomb per second

CHARGE: a fundamental concept needed to explain electric and magnetic phenomena; measured in coulombs

CONDUCTORS: substances through which current can flow without any side effects such as heat

CURRENT: a flow of charges; measured in amperes

DIRECT CURRENT: a current that does not change its magnitude or direction in time; measured in amperes

ELECTRONS: negatively charged particles present in all atoms; the charge of an electron is 1.6 x 10^-19 coulombs

INSULATORS: substances that prevent flow of electricity through them

Bibliography

Becker, Richard. ELECTROMAGNETIC FIELDS AND INTERACTIONS. Reprint. New York: Dover, 1982. A good mathematical treatment of electric and magnetic fields at a moderate level. Contains a good introductory treatment of vectors and tensors and has solutions to several exercises for self study.

Feynman, Richard P., Robert B. Leighton, and Matthew Sands. THE FEYNMAN LECTURES ON PHYSICS. 3 vols. Reading, Mass.: Addison-Wesley, 1963-1965. Contains the lectures given by a great physicist to undergraduates at the California Institute of Technology. Excellent introduction to the basic principles of electricity and magnetism. Provides both engineering and physics viewpoints through topics such as alternating current circuits and the atomic nature of electricity and magnetism.

Jackson, John D. CLASSICAL ELECTRODYNAMICS. New York: John Wiley & Sons, 1975. A standard graduate-level textbook on electricity and magnetism. Contains a very rigorous mathematical treatment of electric and magnetic phenomena. Scope is beyond the standard boundary value problems, and includes topics from atomic and nuclear physics. Includes difficult exercises on various topics.

Maxwell, James Clerk. A TREATISE ON ELECTRICITY AND MAGNETISM. 2 vols. 3d ed. New York: Dover, 1954. The first book on electromagnetic wave theory. It is historically important, but at times contains technical sections. Several concepts are introduced through experimental research.

Ritz, J. R., F. J. Milford, and R. W. Christy. FOUNDATIONS OF ELECTROMAGNETIC THEORY. Reading, Mass.: Addison-Wesley, 1979. This book is addressed to advanced undergraduate physics majors and presents basic concepts in electricity and magnetism, with a qualitative understanding of atomic physics. Good emphasis is shown in deriving the concepts through experimental laws, thereby making them less abstract.

Rojansky, Vladimir. ELECTROMAGNETIC FIELDS AND WAVES. Englewood Cliffs, N.J.: Prentice-Hall, 1971. Written with outstanding clarity and simplicity in the exposition of fundamentals, this book helps to visualize all basic concepts of electricity and magnetism. Highly recommended undergraduate textbook.

Faraday's induced current experiment

Like charges repel each other; opposite charges attract

The Structure of the Atomic Nucleus

Conductors and Resistors

Electrons and Atoms

Forces on Charges and Currents

Insulators and Dielectrics

Motors and Generators