Electromagnetism

• Type of physical science: Classical physics
• Field of study: Electromagnetism

Electromagnetism is the theoretical framework that describes the dynamical effects that a collection of electric charges (at rest or in relative motion) has on other charges. The consequences of this theory include descriptions of a diverse range of phenomena, including the prediction of electromagnetic waves of which visible light is an example.

Overview

Electromagnetism is a study of the effects that a distribution of electric charges has on its surroundings, including its interactions with other electric charges. Representing one of the great syntheses of science, electromagnetism brings together previously separate electric, magnetic, and optical sciences into a single theoretical framework through a set of unifying underlying principles.

It is well known that electric charges come in two varieties, where "like" charges (charges of the same kind) repel each other and "unlike" charges (charges of different kinds) attract each other. The two types of electric charges are conveniently labeled as positive and negative, a label that allows electric charges to be described by a conservation principle known as conservation of charge. This principle states that a net charge can be neither created nor destroyed. Rather, the net charge prior to a reaction must be equal to the net charge after the reaction.

An essential concept that distinguishes electromagnetism from other disciplines of study such as Newtonian mechanics is the concept of the field. Whereas Newtonian mechanics views forces in terms of action at a distance (that is, the Moon is attracted by the distant Earth), with electromagnetism action is viewed locally. For example, if an electric field exists at a position P in space, then an electric charge q located at that position experiences an electric force, resulting from its own charge and from the electric field at position P.

Analogously, the Moon experiences a gravitational force because of its mass, and the gravitational field at its location results from Earth.

Coulomb's law states that two point charges experience an electrostatic force between them, which is proportional to the magnitude of each charge and inversely proportional to the square of the distance between them. In terms of the electric field concept, this can be viewed as the value of one of the charges times the influence that the other charge has on the space at the location of the first charge. This influence that a charge has on the space around it is known as its electric field, which, for a point charge, is proportional to the charge and inversely proportional to the square of the distance from it. The electric field for a charge distribution is often illustrated in terms of diagrams containing electric field lines. These electric field lines are merely convenient schematic representations, much as lines drawn to signify the flow of water in a stream are a schematic representation of the actual flow of the water. By convention, these electric field lines caused by charges at rest always begin on positive charges and always end on negative charges.

Likewise, the magnetic field is the influence that moving electrical currents have on the space around them such that other moving electric charges interact with the magnetic field, thus experiencing a resulting force. The magnetic field can also be schematically represented by magnetic field lines. Nevertheless, magnetic field lines do not begin or end on magnetic charges.

Rather, in contradistinction to electric field lines, magnetic field lines always form closed loops.

This results from the fact that, unlike electric charges, there seem to be no individually observed magnetic charges (known as magnetic monopoles). This can be demonstrated by a bar magnet, which always has a north and south pole. If the magnet is cut in half, then two smaller magnets are created, each with a north and a south pole. The poles cannot be isolated. Yet, it should be noted that there is no reason, on theoretical grounds, to support the nonexistence of magnetic monopoles.

There are a variety of individuals who made significant contributions to what ultimately became known as electromagnetism. These contributions, important in their own right, were subsequently gathered (and, in one case, modified) by James Clerk Maxwell (1831-1879) and are known as the Maxwell equations. The four basic principles making up this collection of equations include Gauss's law for electricity, Gauss's law for magnetism, Faraday's law of induction, and Ampere's law (as modified by Maxwell).

Gauss's law is a reformulation of Coulomb's law. It simply relates the electric field in a geometric way to the electric charges that are present. This is done by comparing the electric flux through an imaginary closed surface (a surface with no edge, such as a sphere or a cube) to the charges present inside that surface. For example, consider an imaginary sphere around a point charge located at its center. Gauss's law simply relates the flux through this surface to the charge contained within the sphere. The greater the charge enclosed by the sphere, the greater the flux through the sphere. Gauss's law for the magnetic field states that the magnetic flux through any closed surface is zero, which is equivalent to the nonexistence of magnetic monopoles.

To illustrate Faraday's law of induction, consider sweeping a closed loop of wire through a magnetic field. The result of this motion is to induce a voltage that will cause an electric current to flow in the wire loop. This effect is one consequence of Faraday's law.

Deduced independently in England by Michael Faraday (1791-1867) and in the United States by Joseph Henry (1797-1878), Faraday's law recognizes that an induced voltage (known as an electromotive force, or emf) may be developed in a coil of wire by changing the magnetic flux passing through this coil. Here, the coil defines an open surface. For example, a wire loop in the shape of a circle bounds a circular area, which is an open surface. It has an edge. A closed surface as used in Gauss's law has no edge. Faraday's law relates the electromotive force generated in the wire loop to the time varying magnetic flux through an open surface bounded by the wire loop, that is, a voltage generated as a result of the effect of a magnetic field on a wire. In cases where the time varying magnetic flux is caused solely by a time-varying magnetic field, however, Faraday's law relates that time varying magnetic field to a resulting induced electric field; that is, a changing magnetic field induces an electric field.

If one were to hold an ordinary magnetic compass near a wire in which a steady direct current (DC) were flowing, then one would notice that the direction in which the compass pointed would not be north necessarily, but rather it would be affected by the current in the wire.

This effect is one consequence of Ampere's law, which plays the same role in magnetostatics that Gauss's law plays for electrostatics. As does Gauss's law, Ampere's law makes use of geometry, in this case, to relate the magnetic field around an imaginary closed loop path to the electric current passing through that closed path. The greater the current through the loop, the stronger the resulting magnetic field.

Of the four principles, both Faraday's law and Ampere's law establish a connection between electric and magnetic phenomena. Gauss's law for the electric field is concerned only with electric charges. Likewise, Gauss's law for the magnetic field is concerned only with the lack of magnetic monopoles. Nevertheless, these four principles are incomplete; they do not explain electromagnetism thoroughly. Maxwell brought together the four principles and synthesized them into a coherent theory of electromagnetism. Vital to this synthesis was the important observation that Ampere's law did not fully describe the relationship between the magnetic field and sources responsible for it. Although Faraday's law describes the induced electric field caused by a time-varying magnetic flux, Ampere's law does not contain a comparable term allowing for an induced magnetic field caused by a time-varying electric flux.

This additional term, dubbed the "displacement current" (which is not a current, at least not in the usual sense), introduces a symmetry between Faraday's law and Ampere's law. Faraday's law predicts the existence of an induced electric field caused by a changing magnetic field and the modified Ampere's law (which is now referred to as the Ampere-Maxwell law) predicts that a changing electric field induces a magnetic field.

The recognition that time-varying electric and magnetic fields can induce each other continually led to the prediction of electromagnetic waves that propagate at the speed of light. In fact, light is merely the continual propagation of time-varying electric and magnetic fields that mutually induce each other. Furthermore, the value of the speed of light is determined by proportionality constants contained in Gauss's law and Ampere's law, which are defined solely in terms of static phenomena: The electric permittivity (the proportionality constant of Gauss's law, where charges are at rest) and magnetic permeability (the proportionality constant of Ampere's law, where electric current is constant). Hence, Maxwell's displacement current not only completed the unification of the sciences of electricity and magnetism contributed to by Faraday and Ampere and others but also brought the science of optics into this unification.

Applications

Electromagnetic waves are a consequence of combining Faraday's law with the Ampere-Maxwell law. From Faraday's law, a time-varying magnetic field induces an electric field, and from the Ampere-Maxwell law, a time-varying electric field induces a magnetic field.

The mathematical combination of these two laws results in a classical wave equation for the electric field and for the magnetic field. The solutions of these equations are electromagnetic waves composed of electric and magnetic fields that are continually inducing each other with a propagation velocity of the speed of light. The prediction of electromagnetic waves was subsequently confirmed by Heinrich Hertz (1857-1894), who generated and detected radio waves in the laboratory and confirmed that they propagate at the free space speed of visible light.

Visible light is an example of propagating electromagnetic waves. These, as well as other electromagnetic waves, are characterized by a frequency. Just as the frequency of a sound wave determines its pitch, the frequency of a monochromatic (single frequency) light beam characterizes its color. For example, a typical beam of light from a helium-neon laser has a frequency of 4.74 x 10¹⁴ hertz. This light is characteristically red. The electric field associated with light waves interacts with the cone cells in the retina of the human eye, with the frequency of this electric field wave producing the sensation of color. Nevertheless, visible light is a small portion of the electromagnetic spectrum. Other forms of electromagnetic waves are radio, infrared, ultraviolet, X-rays, and even γ rays, with each of these types of waves having characteristic applications.

In particular, consider the radio part of the electromagnetic spectrum. An application is radio and television communications. Radio waves can be generated by oscillating electric charges (as, for example, electrons in a transmitting antenna). The radio waves can carry information either by modulating (changing) the amplitude (AM radio) or the frequency (FM radio) of the wave. A receiver with appropriate antenna and electrical circuitry can detect and amplify the electromagnetic signal, decode the information carried on the signal, and display the information. Television viewing is a result of encoded information that rides on a carrier electromagnetic wave as it propagates from the transmission tower to the television set.

Radio astronomy is the study of the universe in the radio part of the electromagnetic spectrum. Quasars (quasi-stellar radio sources) are perhaps the most distant structures in the universe, and they are prodigious radio emitters. The mechanism that produces such strong radio emissions from quasars is still not well understood. Furthermore, the Sun and even the planet Jupiter emit electromagnetic energy in the radio part of the spectrum.

Electrical energy generated by the electric utilities is a classic example of electromagnetic induction, as described by Faraday's law. In nearly all cases, an electrical power plant uses either thermodynamical or mechanical energy sources to turn a shaft. A series of connected wire loops is mounted on that shaft. Sweeping these wire loops through a static magnetic field induces an emf in the wires and, therefore, produces an electrical current in the loops. This is how electrical power is generated for most cities. Another, simple example is the electromagnet. This is a device that generates a sizable magnetic field with the application of a modest electrical current. Consider a piece of iron shaped into a solid cylinder. Insulated electrical wire is then wrapped several times around the iron cylinder and connected to a battery or DC generator. A small current flowing through the wire loops produces a modest magnetic field. Yet, this magnetic field tends to induce a substantially stronger resulting magnetic field by aligning most of the little magnetic fields contained in the ferromagnetic iron. As a result, a substantially larger magnetic field is generated. Resultant magnetic fields with orders of magnitude greater than the magnetic fields as a result of the current alone can be generated this way.

The principle of the transformer is based upon electromagnetic induction, as described by Faraday's law and Ampere's law. Transformers are devices that transfer and convert an alternating voltage from a "primary" circuit to another "secondary" circuit by taking advantage of magnetic induction. A wire wrapped into a series of loops carrying a current (primary circuit) generates a magnetic field that affects charges in another coil of wire (secondary circuit) not physically connected to the first set of loops. If the magnetic field varies with time (as is the case with an alternating current, AC), then the secondary loops of wire experience an AC voltage generated in them as a result of the changing magnetic field generated by the primary circuit. The actual induced voltage is governed by the ratio of the number of loops in the secondary to the primary coils. In this way, it is relatively simple to step up voltages for transmission of electrical energy over long distances and to step down the voltage for local distribution to houses and the like for consumer use.

Context

At present, there appear to be four fundamental forces of nature: gravitation, electromagnetism, the strong nuclear force, and the weak nuclear force. Classical electromagnetism is the theoretical framework that describes phenomena specifically caused by the electromagnetic force within the classical domain of validity, which extends to, but does not include, atomic dimensions. In this regard, electromagnetism is one of the essential "core" areas of physics that includes classical mechanics, thermodynamics, statistical mechanics, electrodynamics, and quantum mechanics. Furthermore, it is the basis of electrical engineering.

All electrical applications are fundamentally governed by the principles of electromagnetism.

Electromagnetism as a field theory is a complete and successful theory within its domain of validity. Moreover, electromagnetism is the archetypical field theory upon which the inspirations for other field theories are often based. That domain of validity, however, does not include atomic-level phenomena, where the electromagnetic interaction is most dominant. The theory that generalizes electromagnetism to include atomic and subatomic-level phenomena involving only the electromagnetic interaction is quantum electrodynamics, or QED for short.

QED is also a field theory not without a sizable inspiration from classical electromagnetism and which reduces to classical electromagnetism at macroscopic dimensions. Today, QED is arguably the most accurate and successful theory ever constructed. At present, QED predicts results that are in agreement with experiment to as many as eleven significant figures. As pointed out by Richard P. Feynman, that is analogous to predicting the distance from Los Angeles to New York City to within the thickness of one human hair. Most attempts at grand unification theories (GUTs) employ the field theoretical approach exemplified by classical electromagnetism. Indeed, electromagnetism is, perhaps, the first major successful unification theory where electricity, magnetism, and optics were brought under the umbrella of Maxwell's equations.

Nevertheless, as a field theory, electromagnetism is plagued by a difficulty characterized by field theories in general. In the case of electromagnetism, one source particle for the electric field is the electron. The electron is a point particle. At present, it does not appear to have any spatial structure. According to the mathematics underlying the theory, an infinite self-energy is required to contain a finite amount of charge within an infinitesimal value. Hence, electrons would appear to have an infinite self-energy, an intolerable situation from the point of view of the theoretical physicist but of little impact to the practicing electrical engineer. Despite this difficulty, electromagnetism has undoubtedly been one of the most remarkably successful theories in the history of science.

Principal terms

CHARGE: the intrinsic property of matter that is responsible for all electromagnetic phenomena

CURRENT: movement of one kind of charge relative to another

ELECTRIC FIELD: the influence that a distribution of charges has on the space around it such that the force experienced by a small test charge q is given by the value of that charge times the electric field, which results from the charge distribution

ELECTROMAGNETIC WAVE: time-varying electric and magnetic fields propagating through space (or through a medium); light is an example of an electromagnetic wave

ELECTROMOTIVE FORCE (EMF): the potential difference between two points (or terminals) of a device that is used as a source of electrical energy

ELECTROSTATIC: refers to situations where electric charges are at rest

FLUX: the value of the electric (or magnetic) field multiplied by the surface area that it crosses

FREQUENCY: the number of cycles or oscillations occurring during a unit of time; a standard unit of frequency is the hertz, which stands for one cycle per second

MAGNETIC FIELD: the influence that a distribution of electric currents has on the space around it

MAGNETOSTATIC: refers to magnetic fields that result from constant electric currents

Bibliography

Feynman, Richard P., Robert B. Leighton, and Matthew Sands. The Feynman Lectures on Physics. New Millennium ed., Basic Books, 2011.

Griffiths, David J. Introduction to Electrodynamics. 5th ed., Cambridge University Press, 2023.

Hewitt, Paul G. Conceptual Physics. 13th ed., Pearson, 2021.

Segre, Emilio. From Falling Bodies to Radio Waves: Classical Physicists and Their Discoveries. Dover Publications, 2007.

Weinberg, Steven. The Discovery of Subatomic Particles. Revised ed., Cambridge University Press, 2003.