Electromagnetism

Electromagnetic fields

The phenomena of electromagnetism is described mathematically using electromagnetic fields. An electromagnetic field (also EM field) is a physical field, varying in space and time, that represents the electric and magnetic influences generated by and acting upon electric charges. The field at any point in space and time can be regarded as a combination of an electric field and a magnetic field. Because of the interrelationship between the fields, a disturbance in the electric field can create a disturbance in the magnetic field which in turn affects the electric field, leading to an oscillation that propagates through space, known as an electromagnetic wave.

There are 6 mathematical quantities which are used to describe electromagnetic fields in 3 distinct cases. The electric field, E, and magnetic flux density, B are used to describe the electromagnetic fields in cases where all the charges are known directly such as the electromagnetic field in a vacuum. To describe the case where the charges inside of a material respond to applied electric and magnetic fields, it is useful to define the electric displacement field, D and magnetic field strength, H, in addition to E and B. Finally, it is sometimes useful to describe electromagnetic fields not in terms of force but in terms of potential energy and momentum. In this case, the electromagnetic field is represented by the electric potential, V, and the magnetic vector potential, A, respectively.

Force on an electric charge due to electromagnetic fields

The force, F. on a charge particle of charge q moving at speed v in an electromagnetic field is given by the Lorentz force(SI definition of quantities): ${\displaystyle \mathbf{F}=q\left(\mathbf{E}+\mathbf{v}\times \mathbf{B}\right)}$

Here, × is the vector cross product, and all quantities in bold are vectors.

The Lorentz force can be used to define both the electric field E and the magnetic flux density B.

Electromagnetic fields in matter

When dealing with electromagnetic fields in matter it is often useful to introduce 2 other fields, in addition to E and B. Since matter is made of particles with both electric charge and intrinsic magnetic moment it responds to an applied electromagnetic field to produce its own electromagnetic field. The details are complicated but often can be described by introducing an electric displacement field, D to complement E and a magnetic field strength, H, to complement B.

Electric potential formulation

In advanced formulations of electromagnetism and to simplify certain calculations it is often useful to reformulate the electromagnetic field in terms of electric potential energy and momentum instead of force. Here, the electromagnetic fields of interest are the electric potential, V, and the magnetic vector potential A. These are related to E and B by: $${\displaystyle \begin{array}{cc}\mathbf{E}& =-\mathrm{\nabla }V-\frac{\mathrm{\partial }\mathbf{A}}{\mathrm{\partial }t}\\ \mathbf{B}& =\mathrm{\nabla }\times \mathbf{A}\end{array}}$$ where ∇ is the gradient, ∇⋅ is the divergence, and ∇× is the curl.

Electrostatics

Electrostatics is a branch of physics that studies slow-moving or stationary electric charges on macroscopic objects where quantum effects can be neglected. Under these circumstances, the electric field, electric potential, and the charge density are related without complications from magnetic effects.

Since classical antiquity, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word ḗlektron (ἤλεκτρον), meaning 'amber', was thus the root of the word electricity. Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulomb's law.

There are many examples of electrostatic phenomena, from those as simple as the attraction of plastic wrap to one's hand after it is removed from a package, to the apparently spontaneous explosion of grain silos, the damage of electronic components during manufacturing, and photocopier and laser printer operation.

Magnetostatics

Magnetostatics is the study of magnetic fields in systems where the currents are steady (not changing with time). It is the magnetic analogue of electrostatics, where the charges are stationary. The magnetization need not be static; the equations of magnetostatics can be used to predict fast magnetic switching events that occur on time scales of nanoseconds or less. Magnetostatics is even a good approximation when the currents are not static – as long as the currents do not alternate rapidly. Magnetostatics is widely used in applications of micromagnetics such as models of magnetic storage devices as in computer memory.

Electrodynamics

In 1600, William Gilbert proposed, in his De Magnete, that electricity and magnetism, while both capable of causing attraction and repulsion of objects, were distinct effects. Mariners had noticed that lightning strikes had the ability to disturb a compass needle. The link between lightning and electricity was not confirmed until Benjamin Franklin's proposed experiments in 1752 were conducted on 10 May 1752 by Thomas-François Dalibard of France using a 40-foot-tall (12 m) iron rod instead of a kite and he successfully extracted electrical sparks from a cloud.

One of the first to discover and publish a link between human-made electric current and magnetism was Gian Romagnosi, who in 1802 noticed that connecting a wire across a voltaic pile deflected a nearby compass needle. However, the effect did not become widely known until 1820, when Ørsted performed a similar experiment. Ørsted's work influenced Ampère to conduct further experiments, which eventually gave rise to a new area of physics: electrodynamics. By determining a force law for the interaction between elements of electric current, Ampère placed the subject on a solid mathematical foundation.

A theory of electromagnetism, known as classical electromagnetism, was developed by several physicists during the period between 1820 and 1873, when James Clerk Maxwell's treatise was published, which unified previous developments into a single theory, proposing that light was an electromagnetic wave propagating in the luminiferous ether. In classical electromagnetism, the behavior of the electromagnetic field is described by a set of equations known as Maxwell's equations, and the electromagnetic force is given by the Lorentz force law.

One of the peculiarities of classical electromagnetism is that it is difficult to reconcile with classical mechanics, but it is compatible with special relativity. According to Maxwell's equations, the speed of light in vacuum is a universal constant that is dependent only on the electrical permittivity and magnetic permeability of free space. This violates Galilean invariance, a long-standing cornerstone of classical mechanics. One way to reconcile the two theories (electromagnetism and classical mechanics) is to assume the existence of a luminiferous aether through which the light propagates. However, subsequent experimental efforts failed to detect the presence of the aether. After important contributions of Hendrik Lorentz and Henri Poincaré, in 1905, Albert Einstein solved the problem with the introduction of special relativity, which replaced classical kinematics with a new theory of kinematics compatible with classical electromagnetism. (For more information, see History of special relativity.)

In addition, relativity theory implies that in moving frames of reference, a magnetic field transforms to a field with a nonzero electric component and conversely, a moving electric field transforms to a nonzero magnetic component, thus firmly showing that the phenomena are two sides of the same coin. Hence the term "electromagnetism". (For more information, see Classical electromagnetism and special relativity and Covariant formulation of classical electromagnetism.)

Today few problems in electromagnetism remain unsolved. These include: the lack of magnetic monopoles, Abraham–Minkowski controversy, the location in space of the electromagnetic field energy, and the mechanism by which some organisms can sense electric and magnetic fields.

Extension to nonlinear phenomena

The Maxwell equations are linear, in that a change in the sources (the charges and currents) results in a proportional change of the fields. Nonlinear dynamics can occur when electromagnetic fields couple to matter that follows nonlinear dynamical laws. This is studied, for example, in the subject of magnetohydrodynamics, which combines Maxwell theory with the Navier–Stokes equations. Another branch of electromagnetism dealing with nonlinearity is nonlinear optics.

Quantities and units

Here is a list of common units related to electromagnetism:

• ampere (electric current, SI unit)
• coulomb (electric charge)
• farad (capacitance)
• henry (inductance)
• ohm (resistance)
• siemens (conductance)
• tesla (magnetic flux density)
• volt (electric potential)
• watt (power)
• weber (magnetic flux)

In the electromagnetic CGS system, electric current is a fundamental quantity defined via Ampère's law and takes the permeability as a dimensionless quantity (relative permeability) whose value in vacuum is unity. As a consequence, the square of the speed of light appears explicitly in some of the equations interrelating quantities in this system.

Formulas for physical laws of electromagnetism (such as Maxwell's equations) need to be adjusted depending on what system of units one uses. This is because there is no one-to-one correspondence between electromagnetic units in SI and those in CGS, as is the case for mechanical units. Furthermore, within CGS, there are several plausible choices of electromagnetic units, leading to different unit "sub-systems", including Gaussian, "ESU", "EMU", and Heaviside–Lorentz. Among these choices, Gaussian units are the most common today, and in fact the phrase "CGS units" is often used to refer specifically to CGS-Gaussian units.

Applications

The theory of electromagnetism is used to understand and design electric circuits, magnetic circuits, and semiconductor devices.

History

Ancient world

Investigation into electromagnetic phenomena began about 5,000 years ago. There is evidence that the ancient Chinese, Mayan, and potentially even Egyptian civilizations knew that the naturally magnetic mineral magnetite had attractive properties, and many incorporated it into their art and architecture. Ancient people were also aware of lightning and static electricity, although they had no idea of the mechanisms behind these phenomena. The Greek philosopher Thales of Miletus discovered around 600 B.C.E. that amber could acquire an electric charge when it was rubbed with cloth, which allowed it to pick up light objects such as pieces of straw. Thales also experimented with the ability of magnetic rocks to attract one other, and hypothesized that this phenomenon might be connected to the attractive power of amber, foreshadowing the deep connections between electricity and magnetism that would be discovered over 2,000 years later. Despite all this investigation, ancient civilizations had no understanding of the mathematical basis of electromagnetism, and often analyzed its impacts through the lens of religion rather than science (lightning, for instance, was considered to be a creation of the gods in many cultures).

19th century

Electricity and magnetism were originally considered to be two separate forces. This view changed with the publication of James Clerk Maxwell's 1873 A Treatise on Electricity and Magnetism in which the interactions of positive and negative charges were shown to be mediated by one force. There are four main effects resulting from these interactions, all of which have been clearly demonstrated by experiments:

1. Electric charges attract or repel one another with a force inversely proportional to the square of the distance between them (Coulomb's law): opposite charges attract, like charges repel.
2. Magnetic poles (or states of polarization at individual points) attract or repel one another in a manner similar to positive and negative charges and always exist as pairs: every north pole is yoked to a south pole.
3. An electric current inside a wire creates a corresponding circumferential magnetic field outside the wire. Its direction (clockwise or counter-clockwise) depends on the direction of the current in the wire.
4. A current is induced in a loop of wire when it is moved toward or away from a magnetic field, or a magnet is moved towards or away from it; the direction of current depends on that of the movement.

In April 1820, Hans Christian Ørsted observed that an electrical current in a wire caused a nearby compass needle to move. At the time of discovery, Ørsted did not suggest any satisfactory explanation of the phenomenon, nor did he try to represent the phenomenon in a mathematical framework. However, three months later he began more intensive investigations. Soon thereafter he published his findings, proving that an electric current produces a magnetic field as it flows through a wire. The CGS unit of magnetic induction (oersted) is named in honor of his contributions to the field of electromagnetism. His findings influenced French physicist André-Marie Ampère's developments of a single mathematical form to represent the magnetic forces between current-carrying conductors.

This unification, which was observed by Michael Faraday, extended by James Clerk Maxwell, and partially reformulated by Oliver Heaviside and Heinrich Hertz, is one of the key accomplishments of 19th-century mathematical physics. It has had far-reaching consequences, one of which was the understanding of the nature of light. Unlike what was proposed by the electromagnetic theory of that time, light and other electromagnetic waves are at present seen as taking the form of quantized, self-propagating oscillatory electromagnetic field disturbances called photons. Different frequencies of oscillation give rise to the different forms of electromagnetic radiation, from radio waves at the lowest frequencies, to visible light at intermediate frequencies, to gamma rays at the highest frequencies.