8 junio, 2024

Electrodynamics: what it is, fundamentals, laws, applications

We explain what electrodynamics is, its history, fundamentals, main laws, and applications

what is the electrodynamics?

The electrodynamics It is the branch of physics that deals with everything related to the movement of electric charges. Describes the evolution over time of a set of N particles with mass and electric charge, whose initial position and speed are known.

If it is a large set of particles with momentum small, their motion and the interactions that take place between them are described macroscopically through classical electrodynamics, which makes use of Newton’s laws of motion and Maxwell’s laws.

And if the momentum of the particles is large and the number of particles is small, relativistic and quantum effects must be taken into account.

Adding the relativistic and quantum effects to the study of the system depends on the energy of the photons involved during the interaction. Photons are particles without charge or mass (for practical purposes) that are exchanged whenever there is an electrical attraction or repulsion.

If the momentum of the photons is small, compared to the momentum of the system, the classical description is sufficient to obtain its characterization.

Brief history of electrodynamics

The laws that describe the dynamics of charged particles were discovered between the end of the 18th century and the middle of the 19th century, when the concept of electric current arose, as a result of the experimental and theoretical work of many scientists.

The Italian physicist Alessandro Volta (1745-1827) made the first voltaic battery at the dawn of the 19th century. With it he obtained a direct current, the effects of which began to be studied immediately.

The link between electric charges in motion and magnetism was revealed with the experiments of the physicist Hans Christian Oersted (1777-1851) in 1820. In them it was observed that an electric current was capable of moving the compass needle of the same way as magnets.

It was André Marie Ampere (1775-1836) who mathematically established the link between current and magnetism, through the law that bears his name.

Simultaneously, Georg Simon Ohm (1789-1854) quantitatively studied the way in which materials conduct electricity. He also developed the concept of electrical resistance and its relation to voltage and current, through Ohm’s law for circuits.

Michael Faraday (1791-1867) found a way to generate a current through relative motion between the source of the magnetic field and a closed circuit.

Some time later, the physicist James Clerk Maxwell (1831-1879) created a theory for electromagnetism that unified all the discovered laws, explaining the phenomena known until then.

Furthermore, through his equations, Maxwell predicted various effects that were later confirmed. For example, when Heinrich Hertz (1857-1894), discoverer of radio waves, verified that they moved at the speed of light.

With the advent of the theory of relativity, at the beginning of the 20th century, it was possible to explain the behavior of particles with speeds close to that of light. Meanwhile, quantum mechanics refined electrodynamics by introducing the concept of spin and thus explaining the origin of magnetism in matter.

Fundamentals of Electrodynamics

Electrodynamics is based on four laws, which are separately known as: Coulomb’s law, Gauss’s law, Ampere’s law, and Faraday’s law.

These four laws, plus the principle of conservation of charge, which is derived from them, and the Lorentz force law, describe how electric charges interact from the classical point of view (without considering the photon as a mediator).

If the speed of the particles is close to that of light, their behavior is modified and it is necessary to add some relativistic corrections to the classical theory that derive from Albert Einstein’s theory of relativity (relativistic electrodynamics).

And when the scale of the phenomena to be studied is the atomic scale or smaller, quantum effects become relevant, giving rise to the quantum electrodynamics.

Mathematical foundations of electrodynamics

The mathematics necessary for the study of electrodynamics are vector algebra and vector calculus, since the electric and magnetic fields are entities of a vector nature. Scalar fields are also involved, such as electric potential and magnetic flux.

The mathematical operators for the derivatives of vector functions are:

Gradient.
Divergence.
Rotational.
Laplacian.

Coordinate systems are required for the resolution of Maxwell’s equations. In addition to Cartesian coordinates, the use of cylindrical coordinates and spherical coordinates is frequent.

In the integration appear the theorems of Green, Stokes and the theorem of divergence.

Finally, there is a function called dirac deltawhich is defined through its properties and is very useful to express charge distributions confined to a certain dimension, for example a linear, superficial distribution, a point or a plane.

electromagnetic waves

The origin of electromagnetic waves is in electric charges whose movement is accelerated. A time-varying electric current produces an electric field, described by the vector function AND (x,y,z,t) and in turn produces a magnetic field B. (x,y,z,t).

These fields combine to form the electromagnetic field, in which the electric field gives rise to the magnetic field and vice versa.

laws of electrodynamics

When electric charges are static, there is electrostatic attraction or repulsion between them, while magnetic interaction arises from the movement of charges.

Maxwell’s four equations relate each field to its source, and together with the Lorentz force, form the theoretical basis of electrodynamics.

Gauss’s law

The flow of electric field that leaves a volume enclosed by the closed surface S, is proportional to the net charge enclosed in it:

Where dTO is a differential of area and what is the electrostatic constant. This law is a consequence of Coulomb’s law for the force between electric charges.

Gauss’s law of magnetism

The magnetic field flux through a volume bounded by a closed surface S is zero, because magnetic monopoles do not exist.

Consequently, whenever a magnet is enclosed within a volume delimited by S, the number of field lines entering S is equal to the number of lines leaving:

Faraday’s Law

Michael Faraday discovered that the relative motion between a closed metal loop C and a magnet generates an induced current. The induced voltage (electromotive force) εind, associated with said current, is proportional to the time derivative of the magnetic flux ΦB that crosses the area delimited by the loop:

The minus sign is Lenz’s law, which states that the induced voltage opposes the change in flux that produces it. But the induced emf is the line integral of the electric field along the closed path C, therefore:

Ampere–Maxwell’s law

The circulation of the magnetic field on a curve C is proportional to the total current that encloses the curve. There are two contributions to it: the conduction current I and the displacement current caused by the time variation of the electric flux ΦE:

Where μo and εo are constants, the former is the vacuum permeability and the second the electrical permittivity of vacuum.

Lorentz’s law

Maxwell’s equations describe the relationship between AND, B. and their respective sources, but the dynamics of an electric charge is described by Lorentz’s law or Lorentz force.

She points out that the total force acting on a charge what that moves with speed v in the middle of an electric field AND and a magnetic field B. (not produced by what) is given by:

F = whatAND +qv x B.

applications of electrodynamics

Charges in ordered movement constitute an electric current, which is capable of generating energy to do useful work: turn on light bulbs, move motors, in short, start up numerous devices.

electric power distribution

Electrodynamics makes possible the transmission of electrical energy, through alternating current, from distant places where energy is transformed and generated, to cities, industries and homes.

electronics

Having as its objective the study of charges in motion, electrodynamics is the physical foundation of electronics, which deals with designing devices that, through electronic circuits, make use of the flow of electrical charges to generate, transmit, receive and store electromagnetic signals that contain information.

References

Cosenza, M. Electromagnetism. University of the Andes.
Díaz, R. Electrodynamics: class notes. National university of Colombia.
Figueroa, D. (2005). Series: Physics for Science and Engineering. Volume 6. Electromagnetism. Edited by Douglas Figueroa (USB).
Jackson, JD Classical Electrodynamics. 3rd. Ed. Wiley.
Tarazona, C. Introduction to Electrodynamics. Editorial Manuela Beltrán University.

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