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Charged particle

A charged particle is a fundamental or composite particle that possesses a nonzero electric charge, such as an elementary particle like the electron (with charge -e) or proton (with charge +e), or a composite particle like an alpha particle (with charge +2e).^[1] These particles are ubiquitous in nature and form the basis of electromagnetic interactions, mediating the electromagnetic force—one of the four fundamental forces—through the exchange of photons.^[2] The electric charge of any particle is quantized in integer multiples of the elementary charge e ≈ 1.602 × 10^{-19} coulombs, ensuring no free particle carries a fractional charge relative to this unit.^[3] Charged particles interact continuously with electric and magnetic fields via the Lorentz force, resulting in curved trajectories, acceleration, and the generation of electromagnetic radiation when accelerated, as described by classical electrodynamics.^[4] In electric fields, they experience a force proportional to the field strength and their charge, accelerating oppositely for positive and negative charges.^[5] In magnetic fields, moving charged particles follow helical paths without change in kinetic energy, a principle exploited in devices like cyclotrons and mass spectrometers.^[6] These interactions underpin phenomena ranging from atomic orbital motion to the behavior of plasmas in stars and fusion reactors.^[7]^[8] In particle physics and applications, charged particles include leptons (e.g., electrons, muons) and charged hadrons (e.g., protons, pions), which are accelerated to high energies in colliders to probe fundamental symmetries and forces. They also play vital roles in radiation therapy, where beams of protons or heavy ions deposit energy precisely via the Bragg peak, minimizing damage to surrounding tissue.^[9] Beyond technology, charged particles drive cosmic processes, such as solar wind and galactic magnetic field dynamics, influencing space weather and astrophysical observations.^[10]

Fundamentals

Definition

A charged particle is any subatomic particle or larger entity that carries a net electric charge, either positive or negative, arising from an imbalance of protons and electrons in composite structures or from intrinsic properties in fundamental constituents.^[11]^[12] The concept of charged particles emerged in the late 19th century, with J.J. Thomson's discovery of the electron in 1897 marking the identification of the first subatomic charged particle through experiments with cathode rays.^[13] Unlike neutral particles, which have no net charge and do not directly interact via the electromagnetic force, charged particles experience attraction or repulsion with other charged entities based on the signs of their charges.^[14] Charged particles span a wide range of scales, from fundamental ones like quarks—which carry fractional electric charges of +2/3 or -1/3—and electrons, to composite examples such as ions in plasmas, where atoms or molecules have gained or lost electrons to become positively or negatively charged.^[15]^[16]

Quantization of Charge

The quantization of electric charge refers to the observation that electric charge is not continuous but occurs in discrete, indivisible units. This fundamental property was first suggested by Michael Faraday's laws of electrolysis in the 1830s, which demonstrated that the mass of substances deposited or liberated during electrolysis is proportional to the quantity of electricity passed and that equal quantities of electricity produce equivalent amounts of different substances, implying the existence of discrete "atoms" of charge.^[17]/Electrochemistry/Faradays_Law) The discrete nature of charge was experimentally confirmed by Robert Millikan's oil-drop experiment in 1909, which measured the charges on tiny oil droplets and showed that they were always integer multiples of a fundamental unit, the elementary charge e.^[18] In this experiment, charged droplets were suspended between parallel plates in an electric field, allowing Millikan to balance gravitational and electric forces while accounting for viscous drag, revealing that the charge on each droplet was q = ne, where n is an integer.^[19] The value of the elementary charge is e = 1.602176634 \times 10^{-19} C, as precisely determined through modern measurements.^[20] In the framework of the Standard Model of particle physics, all observed free particles carry electric charges that are integer multiples of e, such as \pm e for electrons and protons or \pm 2e for some ions.^[21] However, quarks, the fundamental constituents of protons and neutrons, possess fractional charges of \pm \frac{1}{3}e or \pm \frac{2}{3}e, yet these are never observed in isolation due to color confinement in quantum chromodynamics, where quarks are perpetually bound within hadrons, resulting in composite particles with integer charges.^[22] This confinement ensures that no free fractional charges exist, maintaining the quantization observed in experiments.^[23] The implications of charge quantization are profound for particle classification, as it underpins the structure of matter in quantum field theory, where electric charge is treated as a conserved quantum number quantized in units of e, facilitating the description of electromagnetic interactions without free fractional charges.^[24] This principle, evolving from Faraday's empirical insights through Millikan's precise measurements to the theoretical consistency of modern quantum field theory, confirms that all detectable charged particles exhibit integer multiples of the elementary charge.^[25]

Properties

Electric Charge

Electric charge is a fundamental intrinsic property of certain subatomic particles that governs their interactions via electromagnetic forces, resulting in attraction between particles of opposite charge and repulsion between those of the same charge.^[26] This property is conserved in all known physical processes, meaning the total electric charge in an isolated system remains constant regardless of interactions or transformations.^[27] The sign of electric charge follows a conventional assignment: protons carry a positive charge denoted as +e, where e is the elementary charge, while electrons carry an equal-magnitude but negative charge of -e.^[28] Composite particles, such as ions, can exhibit net charges that are integer multiples of e; for example, a sodium ion (Na⁺) has a net charge of +e due to the loss of one electron.^[29] Electric charge is quantified in the SI unit of the coulomb (C), defined as the amount of charge transported by a current of one ampere in one second.^[30] The magnitude of electrostatic forces between charged particles is characterized by Coulomb's constant, k = 8.99 \times 10^9 \, \mathrm{N \cdot m^2 / C^2}, which relates the force F to the product of charges q_1 q_2 and the inverse square of their separation r via F = k \frac{|q_1 q_2|}{r^2}.^[31] In the framework of special relativity, electric charge is a Lorentz scalar, remaining invariant under Lorentz transformations between inertial reference frames.^[32] Charge values observed in nature are quantized, appearing in discrete multiples of the elementary charge e ≈ 1.602 × 10^{-19} C.^[33]

Electromagnetic Interactions

Charged particles interact electromagnetically through the exchange of virtual photons, manifesting as electric and magnetic forces that govern their behavior in fields. The fundamental interaction between two stationary point charges q_1 and q_2 separated by a distance r is described by Coulomb's law, which states that the magnitude of the force is F = k_e \frac{|q_1 q_2|}{r^2}, where k_e = \frac{1}{4\pi\epsilon_0} \approx 8.99 \times 10^9 \, \mathrm{N \cdot m^2 / C^2} is the Coulomb constant and \epsilon_0 is the vacuum permittivity.^[34] The force is repulsive for like charges and attractive for opposite charges, directed along the line joining the particles.^[34] For moving charges, the interaction extends beyond pure electrostatics due to relativistic effects, where the electric field is modified and a magnetic field is generated. A charge in motion with velocity \mathbf{v} produces a magnetic field \mathbf{B} that circles around the direction of motion, following the Biot-Savart law in the non-relativistic limit, but fully accounted for in special relativity through the Liénard-Wiechert potentials.^[35] The total force on a charged particle with charge q in combined electric \mathbf{E} and magnetic \mathbf{B} fields is given by the Lorentz force law: \mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B}).^[36] This magnetic component \mathbf{F}_m = q \mathbf{v} \times \mathbf{B} is always perpendicular to both \mathbf{v} and \mathbf{B}, doing no work on the particle but altering its direction. Relativistic corrections to the Coulomb force arise from these field transformations, ensuring consistency across inertial frames, as the pure $1/r^2 electrostatic form applies only in the rest frame of the charges.^[35] When charged particles accelerate, they emit electromagnetic radiation, a process central to phenomena like synchrotron radiation in circular accelerators. For non-relativistic accelerations, the total power radiated by a point charge q with acceleration \mathbf{a} is given by the Larmor formula:

P = \frac{\mu_0 q^2 a^2}{6 \pi c},

where \mu_0 is the vacuum permeability and c is the speed of light.^[37] This radiation is dipole in nature, with intensity peaking perpendicular to the acceleration direction and zero along it, carrying away energy and leading to phenomena such as orbital decay in atomic systems. In relativistic regimes, the formula generalizes to include a \gamma^6 factor, where \gamma = 1/\sqrt{1 - v^2/c^2}, enhancing radiation for high-speed particles as observed in synchrotron sources.^[37] At high energies, electromagnetic interactions can create or destroy charged particle pairs through quantum processes. Pair production occurs when a high-energy photon (hf > 1.022 \, \mathrm{MeV}) interacts with the electric field near an atomic nucleus, converting into an electron-positron pair (e^- e^+), conserving charge and lepton number while the nucleus recoils to balance momentum.^[38] The reverse process, pair annihilation, involves an electron and positron colliding to produce two gamma-ray photons, each with energy at least $0.511 \, \mathrm{MeV} (the electron rest mass energy), emitted oppositely if the pair was at rest.^[38] These QED-mediated events underscore the particle-antiparticle symmetry in electromagnetic interactions, with cross-sections increasing logarithmically above threshold energies.^[38]

Behavior

Motion in Electric Fields

When a charged particle with charge q and mass m enters a uniform electric field \mathbf{E}, it experiences a force \mathbf{F} = q \mathbf{E}, which is independent of the particle's velocity.^[39] This force results in constant acceleration \mathbf{a} = \frac{q \mathbf{E}}{m} along the field direction for non-relativistic speeds.^[40] If the initial velocity is perpendicular to \mathbf{E}, the trajectory becomes parabolic, similar to projectile motion under gravity; for instance, in cathode ray tubes (CRTs), electrons are deflected parabolically by deflecting plates to control beam position on a screen.^[41] The equation of motion in the absence of magnetic fields is m \frac{d\mathbf{v}}{dt} = q \mathbf{E}.^[42] The motion also involves changes in potential energy, as the electric field performs work W = q \Delta V on the particle when it moves through a potential difference \Delta V.^[4] This work converts to kinetic energy, accelerating the particle; in particle accelerators, such as those using radiofrequency cavities, timed electric fields repeatedly boost particle speed by transferring energy from oscillating fields.^[43] In non-uniform electric fields, such as those in quadrupole lenses, particles experience focusing or defocusing effects due to spatially varying \mathbf{E}. Electric quadrupoles produce a linear field gradient, where the force on off-axis particles is proportional to their displacement from the axis, enabling beam collimation in accelerators.^[44] For relativistic speeds, the classical equations no longer hold, and the momentum is \mathbf{p} = \gamma m \mathbf{v}, with the Lorentz factor \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}, where c is the speed of light; the equation of motion becomes \frac{d\mathbf{p}}{dt} = q \mathbf{E}.^[45] This accounts for mass increase and non-linear velocity changes in strong fields.^[46]

Motion in Magnetic Fields

When a charged particle moves in a uniform magnetic field \mathbf{B} with velocity \mathbf{v} perpendicular to \mathbf{B}, the magnetic force \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) causes the particle to follow a circular path known as cyclotron motion. The radius r of this circular orbit, called the Larmor radius or gyroradius, is given by r = \frac{mv}{qB}, where m is the particle's mass, v is the speed perpendicular to \mathbf{B}, q is the charge, and B is the magnetic field strength.^[47] The angular frequency of this motion, termed the cyclotron frequency \omega, is \omega = \frac{qB}{m} and is independent of the particle's speed.^[47] If the initial velocity has a component parallel to \mathbf{B}, denoted v_\parallel, the motion decomposes into uniform straight-line progression along the field lines at constant speed v_\parallel combined with circular gyration in the plane perpendicular to \mathbf{B} due to the perpendicular velocity component v_\perp. This results in a helical path, where the pitch of the helix is h = 2\pi r \frac{v_\parallel}{v_\perp} and the overall speed remains constant.^[48] The magnetic force is always perpendicular to the velocity, performing no work on the particle, so there is no net gain or loss of kinetic energy; only the direction changes.^[49] In nature, such helical trajectories are evident in the aurora borealis, where charged particles from the solar wind, primarily electrons and protons, are guided by Earth's magnetic field toward the polar regions and spiral along geomagnetic field lines, exciting atmospheric atoms to produce visible light emissions.^[50] For relativistic particles, where speeds approach the speed of light, the cyclotron radius modifies to r = \frac{p_\perp}{qB}, where p_\perp = \gamma m v_\perp is the momentum component perpendicular to \mathbf{B}, with the Lorentz factor \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} and v the total speed.^[47] This relation is crucial in cosmic ray detection, as magnetic spectrometers like the Alpha Magnetic Spectrometer (AMS-02) on the International Space Station measure particle rigidity R = p/q from the observed curvature radius in a known B field, enabling identification of cosmic ray origins and composition up to tera-electronvolt energies.^[47]^[51]

Examples

Elementary Particles

In the Standard Model of particle physics, elementary charged particles are the fundamental building blocks that carry electric charge and participate in electromagnetic interactions. These include charged leptons and quarks, which are fermions organized into three generations, along with their antiparticles, as well as the W⁺ and W⁻ bosons. Unlike composite particles, these are point-like and indivisible.^[52] The charged leptons consist of the electron, muon, and tau lepton, each with a charge of -1 times the elementary charge e. The electron has a mass of 0.5109989461(31) MeV/c^2, making it the lightest charged particle and a key component of atomic structure.^[53] The muon, with a mass of 105.6583745(24) MeV/c^2, is heavier and unstable, decaying primarily into an electron, electron antineutrino, and muon neutrino.^[54] The tau lepton, the heaviest at 1776.86 ± 0.12 MeV/c^2, also decays rapidly via weak interactions.^[55] Associated neutrinos—electron neutrino, muon neutrino, and tau neutrino—carry no electric charge and thus are not considered charged particles.^[52] Quarks are the other class of elementary charged fermions, coming in six flavors: up, down, charm, strange, top, and bottom, arranged in three generations. They carry fractional electric charges: up, charm, and top quarks have +2/3 e, while down, strange, and bottom quarks have -1/3 e.^[56] Quarks interact via the strong force in addition to electromagnetic and weak forces, but due to color confinement, they are never observed in isolation and always form bound states like hadrons.^[52] The W⁺ and W⁻ bosons are massive spin-1 bosons that mediate the charged-current interactions of the weak force. They carry electric charges of +e and -e, respectively, and have a mass of 80.379 ± 0.012 GeV/c^2.^[57] The W⁺ and W⁻ are particle-antiparticle conjugates of each other and decay rapidly into lepton-neutrino or quark-antiquark pairs. Every elementary particle has a corresponding antiparticle with opposite charge and other quantum numbers. The positron, the antiparticle of the electron, carries +1 e and was predicted by Paul Dirac's relativistic quantum equation in 1928, which accounted for negative-energy solutions interpreted as antiparticles.^[58] It was experimentally discovered in 1932 by Carl Anderson in cosmic ray tracks.^[59] Antiquarks have charges opposite to their quark counterparts, such as anti-up (-2/3 e) and anti-down (+1/3 e); for example, the antiproton, composed of three antiquarks, has a net charge of -1 e.^[59] The quark model was independently proposed in 1964 by Murray Gell-Mann and George Zweig to explain the structure of hadrons observed in particle accelerator experiments, introducing quarks as fundamental constituents with fractional charges to classify baryons and mesons.^[60]

Composite Particles

Composite particles are bound systems of elementary particles that exhibit a net electric charge due to the imbalance in the charges of their constituents. These include hadrons formed by quarks bound by the strong force, atomic ions resulting from electron gain or loss, and charged atomic nuclei. Unlike elementary particles, the charge of composites emerges from the collective properties of their components, often leading to integer multiples of the elementary charge e. Such particles play crucial roles in nuclear reactions, plasma physics, and everyday chemical processes. Hadrons represent a primary class of charged composite particles, consisting of quarks confined by the strong nuclear force. The proton, a baryon with quark content uud (two up quarks and one down quark), carries a net charge of +e, arising from the charges of its quarks: up quarks each contribute +\frac{2}{3}e, while the down quark contributes -\frac{1}{3}e.^[61]^[62] Mesons, such as the positively charged pion \pi^+ with composition u\bar{d} (up quark and anti-down quark), also exhibit a net charge of +e, as the up quark's +\frac{2}{3}e combines with the anti-down quark's +\frac{1}{3}e.^[63] In contrast, the neutron (quark content udd) is neutral overall but can produce charged particles through beta decay, where a down quark transforms into an up quark, emitting an electron and antineutrino, effectively changing the nuclear charge in composite systems.^[64] Atomic ions form when atoms gain or lose electrons, resulting in net charges while the nucleus remains intact. For instance, the sodium ion \mathrm{[Na](/page/Na)}^+ arises from neutral sodium losing one electron, yielding a charge of +e due to the imbalance between the 11 protons and 10 electrons.^[65] Similarly, the chloride ion \mathrm{Cl}^- forms when chlorine gains an electron, creating a charge of -e with 17 protons and 18 electrons.^[66] In astrophysical contexts, such as stellar interiors, atoms are fully ionized into plasma, where ions like \mathrm{H}^+ (protons) and heavier species carry positive charges, contributing to the electrically conductive state of matter that dominates 99% of the visible universe.^[67] Charged nuclei exemplify composite particles at the nuclear scale, where protons and neutrons bind via the strong force to produce a net positive charge equal to the proton number [Z](/page/Z) \times e. The alpha particle, a helium-4 nucleus (^4_2\mathrm{He}^{2+}), consists of two protons and two neutrons and carries a charge of +2e, making it a key emitter in alpha decay processes. In nuclear fission, such as that of uranium-235, the parent nucleus splits into fragments with variable atomic numbers [Z](/page/Z), typically around 36–56 for thermal neutron-induced fission, resulting in highly charged ions with charges up to approximately +20e or more immediately after scission, before electron capture adjusts them.^[68] Formation of charged composite particles often involves processes that alter the balance of protons, neutrons, or electrons. Ionization in gases occurs when high-energy particles, such as cosmic rays, collide with neutral atoms, ejecting electrons to create ion pairs (e.g., positive atomic ions and free electrons), with each pair requiring about 34 eV in air.^[69] Beta decay provides another mechanism, particularly for nuclei, where a neutron converts to a proton (beta-minus decay), increasing the nuclear charge by +e and emitting an electron, or vice versa in beta-plus decay, as observed in radioactive isotopes.^[70] These processes underpin phenomena from atmospheric electricity to stellar nucleosynthesis.

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Sep 15, 2021 · A plasma is made when the electrons are separated from the outer atomic orbitals of a material, creating a sea of ions and moving charges. ...
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Mass, charge, and kinetic energy of fission fragments - INIS-IAEA
Starting with a given fission-prone nucleus, a binary fission event is rather fully specified one the mass number A, the charge number Z, the kinetic energy ...
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[PDF] Chapter 2: Overview of Atmospheric Ionizing Radiation (AIR)
The high-pressure ion chamber measures the ion current generated by the cosmic rays in the filling gas. The filling gas is usually argon within a steel ...
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Secrets of beta decay unraveled at ISOLDE - CERN EP Newsletter
Dec 9, 2020 · In beta decay an electron (or positron) is emitted from the atomic nucleus. The energy spectrum of the beta particle is continuous, which led to ...