====== Electric charge ====== |< 100% >| | //[[user/Stan Zurek]], Electric charge, Encyclopedia Magnetica//, \\ @PAGEL@ | **Electric charge**, typically denoted by **//Q//**, **//q//** or **//e//** - an intrinsic property of some [[subatomic particle|subatomic particles]] (e.g. [[electron|electrons]] and [[proton|protons]]). Electric charges generate [[electrostatic field|electrostatic]], [[magnetic field|magnetic]] and [[electromagnetic field|electromagnetic fields]], through which forces are exerted on other electrically charged particles.[(Newman>[[https://books.google.co.uk/books?isbn=0387772596|Jay Newman, Physics of the Life Sciences, Springer Science & Business Media, 2010, ISBN 0387772596]])] Electrostatic [[field lines]] around an [[electric dipole]], in which positive and a negative charges attract [[file/electric_charges_magnetica_png|{{electric_charges_magnetica.png}}]] {{page>insert/by_SZ}} Electric charges have only two types: **positive** or **negative**, with the like polarities repelling each other and the opposite ones attracting. Every isolated system fulfils the condition of [[conservation of charge]], so that the total sum of positive and negative charges never changes. This is a fundamental law is the basis for all electromagnetic theory.[(Newman)] Movement of electric charges constitutes [[electric current]]. Electrical forces in atoms determine the physical and chemical properties of matter.[(Purcell)] Scientists can describe, but still cannot explain what exactly is electric charge. However, it is sufficient for such a basic property that it exists, it has some physical meaning and is measurable within the given [[system of units]].[([[http://google.com/books?isbn=9781139451925|Bhag Singh Guru, Hüseyin R. Hiziroglu, Electromagnetic Field Theory Fundamentals, Cambridge University Press, 2004, ISBN 9781139451925]], p. 1)] Opposite charges attract, same charges repel, neutral bodies generate no force (grey) but neutral bodies in the presence of other charges become locally polarised due to [[electrostatic induction]] [[file/electrostatic_force_magnetica_png|{{electrostatic_force_magnetica.png}}]] {{page>insert/by_SZ}} ===== Units of charge ===== In the [[SI system]], the amount of electric charge //**Q**// is measured in **[[coulomb|coulombs]]**, denoted with the symbol "**C**".[(BIPM_2019>[[https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf|Bureau International des Poids et Mesures, The International System of Units (SI), 9th edition, 2019]], {accessed 2021-04-10})] However, the base unit of electricity in the SI system is [[ampere]] (A), which measures electric current //I//. The charge //Q// = 1 C is equal to the amount of charge transferred with the current //I// = 1 A flowing for the time //t// = 1 s. | $$Q = I·t $$ | (A·s) ≡ (C) | The amount of charge is used for example for quantifying [[partial discharge]] phenomena in [[electrical insulation]]. Common values of partial discharges are between 1 pC and 10 nC, with values below 10 pC not leading to harmful effects in the the insulating material.[([[http://www.tauscher.com/html/partialdischarge.html|Tauscher Transformatoren, What is partial discharge?]], {accessed 2021-05-15})][([[https://www.pdix.com/products/partial-discharge-monitoring-systems/icmmonitor.html|Power Diagnostix Systems, ICMmonitor]], {accessed 2021-05-15})] ===== Properties of electric charges ===== For static charges the amount of this force is quantified by [[Coulomb law|Coulomb's law]]. The amount of electric charge is quantised and its smallest unit called **elementary charge** has the value of: **e = 1.602 176 634 × 10−19** [[coulomb]].[(Zyla>[[https://pdg.lbl.gov/2020/citation.html|P.A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020)]] )]. This value is a constant in our universe.[(Britannica>[[https://www.britannica.com/science/electric-charge|Encyclopædia Britannica, Electric charge]], {accessed 2020-10-25} )] A **[[proton]]** has a positive charge of **+e**, and **[[electron]]** to the exactly opposite, negative value of **-e** ([[neutron]] has zero charge). The matching of the amount of the quantum of positive and negative charges is extremely precise to the highest experimental accuracy that can be attained, at the level of 1 part in 1020. If this was not the case then matter would violently disintegrate.[(Purcell>[[http://google.com/books?isbn=9781107014022|E.M. Purcell, D.J. Morin, Electricity and magnetism, 3rd edition, Cambridge University Press, 2013, ISBN 9781107014022]])][(Griffiths>[[http://books.google.com/books?isbn=0321856562|David J. Griffiths, Introduction to electrodynamics, 4th ed., Pearson, Boston, 2013, ISBN 0321856562]])] {{page>insert/paypal}} The electric charges in [[antimatter]] are reversed, with [[positron]] (equivalent of electron) being positive, and [[antiproton]] negative. It is possible for positive and negative charges (e.g. electron and positron) to combine and annihilate, converting to other form of energy. It is also possible for two opposing charges to be produced in some sub-atomic interaction. But such interactions always occur in pairs of positive-negative charges, so that the law of charge conservation never violated.[(Purcell)] For example, during [[radioactivity|radioactive]] decay it is possible for a positron (e+) to be emitted from a proton (e+), which then becomes a neutron so that the amount of electric charge remains constant.[(Holbrow)] Electrically charged particles also exhibit intrinsic [[magnetic moment]]. [[Electron magnetic moment]] is especially strong and is responsible for the phenomenon of [[ferromagnetism]].[(Purcell)] ===== Fields and forces ===== An electric charge generates all of the components of electromagnetic field in the space around itself, depending on the state of motion of the charges:[(Purcell)][(Griffiths)] * charges which are static in space generate [[electrostatic field]] * charges which move at a constant velocity generate [[magnetostatic field]] (due to [[velocity field|velocity fields]]) * charges which are accelerated generate radiating [[electromagnetic field]] (due to [[acceleration field|acceleration fields]]) The presence of a given field can be detect by the amount and direction of mechanical force exerted on another stationary or moving charge ([[test charge]]). The total electromagnetic force on an electric charge is called [[Lorentz force]].[(Holbrow>[[https://books.google.co.uk/books?isbn=9780387790794|Charles H. Holbrow, James N. Lloyd, Joseph C. Amato, Enrique Galvez, M. Elizabeth Parks, Modern Introductory Physics, 2nd ed., Springer, New York, ISBN 9780387790794]])] ==== Electrostatic field ==== The name **[[electrostatic field]]** is used to denote specifically that some **[[electric field]]** does not change with time, because the charges are stationary.[(Griffiths)] An electrostatic field generated by one charge exerts a force on another electric charge, as defined by the [[Coulomb law|Coulomb's law]]:[(Holbrow)] |
$$ \vec F = \frac{1}{4 · π · ε_0} · \frac{q_1 · q_2}{r^2} · \vec {\hat r } $$
| (N) | where: $ε_0$ - [[permittivity of free space]], 8.8541878128 × 10-12 (F/m), $q_1$ and $q_2$ - amount of electric charge (C), $r$ - distance between the charges (m), $\vec {\hat r }$ - [[unit vector]] in the direction of //r//. Each electric charge, or a charged object generates an electric field in the space around itself, and this is typically visualised by field lines, which by convention are directed away from a positive charge and towards the negative charge. The charges are the "sources" of these field lines, so that the lines start and end at the charges. Electrostatic field lines of a positive charge [[file/positive_charge_magnetica_png|{{positive_charge_magnetica.png}}]] {{page>insert/by_SZ}} Electrostatic field of a negative charge [[file/negative_charge_magnetica_png|{{negative_charge_magnetica.png}}]] {{page>insert/by_SZ}} Positive charges repel [[file/positive_charges_magnetica_png|{{positive_charges_magnetica.png}}]] {{page>insert/by_SZ}} Negative charges repel [[file/negative_charges_magnetica_png|{{negative_charges_magnetica.png}}]] {{page>insert/by_SZ}} Electric field //E// acting with a force //Fe// on a positive charge //q// [[file/lorentz_force_electric_magnetica_png|{{lorentz_force_electric_magnetica.png}}]] {{page>insert/by_SZ}} And in a more general case it is the local electric field //E// which generates the force:[(Griffiths)] |
$$ \vec F = q · \vec E $$
| (N) | where: $q$ - charge (C), $\vec E$ - electric field vector (V/m). A positive electric charge (stationary or moving) is accelerated in the direction of the uniform electric field //E//. For a negative charge, the directions are reversed. If the charge is already moving before application of an additional electric field then the acceleration add up vectorially, according to the [[superposition]] rule. ==== Magnetostatic field ==== An electric charge which moves with a constant velocity (without acceleration) produces a **[[magnetic field]]** in the space around itself. For a single moving charge the electric and magnetic field it generates are "attached" to the moving charge (does not radiate away into space), and it is sometimes referred to as [[velocity field]].[(Stohr>[[https://books.google.co.uk/books?isbn=3540302832|Joachim Stöhr, Hans Christoph Siegmann, Magnetism: From Fundamentals to Nanoscale Dynamics, Springer Science & Business Media, 2007, ISBN 3540302832]], p. 105)] If the electric charges are static then they do not generate magnetic field, and also the magnetic force does not act on them. Magnetic field //B// acting with a force //Fm// on a moving positive charge //q// [[file/lorentz_force_magnetic_magnetica_png|{{lorentz_force_magnetic_magnetica.png}}]] {{page>insert/by_SZ}} If there are many moving charges, as for example in a conducting wire, and if the resulting [[electric current]] does not change (in space or time) then the produced field is called **[[magnetostatic field]]**.[(Griffiths)] Magnetostatic field exerts a force on a moving electric charge, which in the absence of electrostatic field is:[(Purcell)] |
$$ \vec F = q · \vec v × \vec B $$
| (N) | where: $q$ - charge (C), $\vec v$ - moving charge velocity vector (m/s), $\vec B$ - magnetic field vector (T). The force generated by magnetic field is often called the **[[magnetic force]]** and is perpendicular to both the direction of movement of the charged body and the direction of the magnetic field, therefore magnetic field do no work (all work is performed by the electric field).[(Griffiths)] Consequently, if the charge is moving parallel to the magnetic field there is no magnetic force acting on it. The magnetic force does not accelerate the charge in a linear way, just deflects its path, and can bend it into a circle, with a radius proportional to the velocity of the charge, its mass and intensity of magnetic field.[(Holbrow)] If the direction of initial movement is not perpendicular to the magnetic field the the trajectory can be helical.[(Coey)] Electric current //**I**// generates [[magnetic field strength]] //**H**// whose vector is always perpendicular to the direction of I, according to the [[right-hand rule]] [[file/Electric_current_generates_magnetic_field_Magnetica_jpg|{{Electric_current_generates_magnetic_field_Magnetica.jpg}}]] {{page>insert/by_SZ}} [[Magnetic field]] around a moving [[electron]] (because of the convention the electron moves in the opposite direction to electric current)[(Maxfield>[[https://books.google.co.uk/books?isbn=9780080949666|C. Maxfield et al., Electrical Engineering: Know It All, Newnes, 2011, ISBN 9780080949666]], p. 1004)] [[file/biot-savart_electron_magnetica_png|{{biot-savart_electron_magnetica.png}}]] {{page>insert/by_SZ}} ==== Electromagnetic field ==== Electric field //E// and magnetic field //B// acting with a force //F = Fe + Fm// on a positive charge //q// [[file/lorentz_force_e_and_b_magnetica_png|{{lorentz_force_e_and_b_magnetica_.png}}]] {{page>insert/by_SZ}} **[[Electromagnetic field]]** (comprising both components, electric and magnetic) is generated by electric charges whose motion is accelerated in a linear, circular, or any other way (with positive or negative acceleration). Such electromagnetic field radiates into space, away from the accelerated charge.[(Purcell)] Such electromagnetic field can be also called [[acceleration field]].[(Stohr)] Electromagnetic field exerts a force on a stationary or moving electric charge, defined by the [[Lorentz force]]:[(Purcell)] |
$$ \vec F = q · \vec E + q · \vec v × \vec B $$
| (N) | where: $q$ - charge (C), $\vec E$ - electric field vector (V/m), $\vec v$ - moving charge velocity vector (m/s), $\vec B$ - magnetic field vector (T). A stationary charge will be moved, because of the electric field, and magnetic field will affect is the path of movement. However, the exact trajectory can be quite complex, depending on the ratio of all the involved quantities, including the direction and velocity of the initial movement. If the electric field is weak, and the magnetic field strong, the charge can move sideways, along a cycloid curve.[(Purcell)] Diagram illustrating generation of [[electromagnetic field]] by an [[electric charge]]: a static charge (grey small circle at the centre) generates [[electrostatic field]] (blue area) which statically extends away into space. A sudden acceleration of the charge (dark blue small circle) creates an electromagnetic pulse (red ring) which [[radiation|radiates]] away into space at the [[speed of light]], and the space far away still contains the electrostatic field from the time when the charge was stationary (as indicated by grey lines). A charge moving at a constant velocity //v// generates electric and magnetic field attached with the charge (green area). The [[field lines]] (black lines) show the direction and intensity of electric field.[(Purcell)] [[file/electromagnetic_field_magnetica_png|{{electromagnetic_field_magnetica.png}}]] {{page>insert/by_SZ}} ===== Electric current ===== By convention, direction of [[electric current]] is from plus to minus of the [[voltage source]], hence opposite to the movement of [[electron|electrons]] [[file/electric_current_e-m_png|{{electric_current_e-m.png}}]] {{page>insert/by_SZ}} [[Electric current]] is defined as a change of electric charge //Q// in time //t//: |
$$ I = \frac{Δ Q}{Δ t} $$
| (A) | Hence, current is a movement of electric charges, in any unbalanced form: individual charged particles (electrons or ions), unbalanced distribution of charges, virtual or [[quasi-particle|quasi-particles]] ([[electron hole|electron holes]]), etc. ==== Magnetic moments ==== From a [[classical physics]] viewpoint, an electron orbiting an atomic [[nucleus]] also constitutes a current, whose value can be calculated knowing dimensions of an atom, speed of orbiting and the value of electric charge of the electron. The analogy of orbital moment is an electron orbiting the nucleus on a circular orbit (left) and for spin the sphere spins around its own axis (right) [[file/orbital_spin_magnetic_moment_em_png|{{orbital_spin_magnetic_moment_em.png}}]] {{page>insert/by_SZ}} Therefore, there is a [[magnetic dipole moment]] associated with the orbit of an electron: [[magnetic orbital moment]]. A spinning electrically charged body will also generate a magnetic field, and this analogy is used as "illustration" of [[magnetic spin moment]] of an electron. However, this classical analogy fails, because [[neutron|neutrons]] also have a magnetic spin moment, even though they have no electrical charge. ==== Quantisation of electric charges ==== Only such sub-atomic particles like [[quark|quarks]] are thought to have electric electric charge in non-integer quantities e.g. -1/3 //e// or +2/3 //e//, but they only exists in configurations which add up to integer values of charge. For example, proton comprises three quarks (//up, up, down//), which add up to +1 //e//. Therefore, in any macroscopic application the charge is always quantised by the elementary amount of 1 e.[(Purcell)][(Tong>[[http://www.damtp.cam.ac.uk/user/tong/em/el1.pdf|David Tong, Electromagnetism, University of Cambridge Part IB and Part II Mathematical Tripos, Lent Term, 2015]], {accessed 2020-10-16} )] Existence of quantised **magnetic charges** ([[magnetic monopole|magnetic monopoles]]) was proposed as a theoretical reason for quantisation of electrical charges. However, despite extensive international research no magnetic monopoles were ever found. ===== Magnetism and electromagnetism ===== |< 100% >| | {{/wiki/logo.png?20&nolink}} //See also: [[Electromagnetism]].// | [[Macroscopic|Macroscopically]] observable [[Magnetic materials|magnetic properties of materials]] arise because of the magnetic quantum properties of electrons ([[spin magnetic moment]] and [[orbital magnetic moment]]), as well as due to the electrostatic interactions between the [[electron orbital|electron orbitals]].[(Coey>[[https://books.google.co.uk/books?isbn=0521816149|J.M.D. Coey, Magnetism and Magnetic Materials, Cambridge University Press, 2010, ISBN 9780521816144]])] Electric charges, electricity, magnetism and electromagnetism are inseparably intertwined. ===== Subatomic particle detection ===== Compact Muon Solenoid (CMS) detector at CERN [[file/cern_alice_cms_slice_png|{{cern_alice_cms_slice.png}}]] //Copyright (c) CERN// Many experiments with radioactive matter were conducted by observing the trajectories of particles moving through magnetic and electric field. Devices such as mass spectrometer utilise these effects. Trajectories of charged particles travelling through magnetic field are bent by the magnetic field due to the [[Lorentz force]]: positive particles are deflected one way, negative particles in the opposite way, but the path of photons or uncharged particles is not affected by magnetic field. Additionally, heavy particles are more difficult to deflect, so knowing the velocity and charge it is possible to deduce mass (or charge if the mass is known).[(Holbrow)] Properties of electrically charged particles are used for detection of sub-atomic particles, in such physical experiments as those carried out in the Large Hadron Collider.[(CMS>[[https://cms.cern/detector|About CMS, CMS.cern]], {accessed 2021-05-12})] The beams of accelerated particles are made to collide inside a detector, which comprises powerful big superconducting [[electromagnet]] (extending over several metres), surrounded by a number of detectors, for sensing various properties of the particles created as an aftermath of the collision. Thousands of single sensors are used around the volume of interest, which allows tracing the trajectories in 3D, and inferring their properties such as momentum, charge, mass, etc.[(ALICE>[[https://alice.cern/|The heavy ion experiment at the Large Hadron Collider]], {accessed 2021-05-12})] Schematic overview of ALICE (A Large Ion Collider Experiment) [[file/cern_alice_run3_jpg|{{cern_alice_run3.jpg}}]] //Copyright (c) CERN// ALICE V0 detector assembly [[file/cern_alice_v0_detector_jpg|{{cern_alice_v0_detector.jpg}}]] //Copyright (c) CERN// ===== See also ===== * [[Magnetism]] * [[Electrostatics]] * [[Magnetostatics]] * [[Electromagnetic field]] * [[Electric field]] * [[Magnetic field]] ===== References ===== ~~REFNOTES~~ {{tag> Electric_charge Electron Proton Neutron Electricity Magnetism Electric_current Counter}}