Meta tags:

Headings (most frequently used words):

electric, fields, field, charge, in, electrostatic, continuous, uniform, of, point, contents, description, mathematical, formulation, electromagnetic, energy, the, displacement, relativistic, effects, on, common, formulas, see, also, references, external, links, electrostatics, superposition, principle, distributions, potential, vs, discrete, representation, parallels, between, and, gravitational, lines, definitive, equation, vector, constitutive, relation, motion, propagation, disturbances, arbitrarily, moving,

Text of the page (most frequently used words):
the (394), mathbf (190), field (152), electric (145), displaystyle (129), and (95), charge (88), #fields (59), that (56), point (50), for (45), frac (45), are (43), charges (42), law (37), varepsilon (36), from (32), magnetic (29), with (28), edit (28), this (27), electromagnetic (27), force (27), where (27), isbn (26), equations (25), time (24), lines (24), potential (23), maxwell (22), which (22), vector (22), between (20), density (20), 978 (19), hat (19), can (19), coulomb (18), given (18), charged (18), surface (17), electrostatic (17), over (17), right (16), particle (16), moving (15), partial (15), left (14), due (14), uniform (13), space (13), positive (13), electromagnetism (12), electricity (12), described (12), faraday (12), not (12), main (12), other (11), two (11), each (11), also (11), direction (11), light (11), when (11), article (11), stationary (10), magnitude (10), times (10), since (10), volume (10), equation (10), speed (10), source (10), unit (10), nabla (10), current (10), university (9), magnetism (9), physics (9), purcell (9), induction (9), total (9), see (9), textstyle (9), negative (9), position (9), particles (9), beta (9), displacement (9), links (8), electrostatics (8), electrodynamics (8), curl (8), any (8), relativistic (8), have (8), sigma (8), uniformly (8), such (8), lorentz (8), gravitational (8), varying (8), per (8), wikipedia (7), terms (7), non (7), link (7), edward (7), david (7), cambridge (7), continuous (7), gauss (7), infinite (7), form (7), region (7), principle (7), permittivity (7), energy (7), both (7), one (7), rho (7), toggle (6), may (6), cs1 (6), external (6), press (6), introduction (6), propagation (6), effects (6), function (6), proportional (6), distance (6), used (6), only (6), distribution (6), same (6), dipole (6), linear (6), lambda (6), static (6), its (6), solution (6), however (6), retarded (6), radiation (6), boldsymbol (6), general (6), points (6), away (6), equal (6), would (6), frame (6), four (6), mathematical (6), free (6), currents (6), these (6), they (6), forces (6), called (6), page (5), location (5), dead (5), description (5), states (5), new (5), oclc (5), cite (5), special (5), square (5), history (5), spherical (5), there (5), formula (5), effect (5), sometimes (5), parallel (5), component (5), tensor (5), material (5), defined (5), represent (5), together (5), resulting (5), line (5), plates (5), voltage (5), varphi (5), superposition (5), move (5), motor (5), contents (4), search (4), view (4), commons (4), maint (4), articles (4), all (4), state (4), media (4), related (4), 2011 (4), 2nd (4), york (4), morin (4), 2013 (4), 3rd (4), john (4), wiley (4), classical (4), griffiths (4), book (4), theory (4), relativity (4), pdf (4), interaction (4), repel (4), flux (4), feynman (4), here (4), conductors (4), axis (4), distributed (4), sphere (4), above (4), physical (4), than (4), motion (4), example (4), case (4), far (4), while (4), represented (4), test (4), their (4), materials (4), into (4), define (4), similarly (4), ampère (4), difference (4), volt (4), describes (4), sum (4), formulation (4), greater (4), hide (4), sidebar (4), subsection (4), text (3), using (3), wikimedia (3), wikidata (3), ignored (3), retrieved (3), international (3), engineering (3), 1999 (3), 139 (3), heaviside (3), waves (3), doi (3), help (3), permanent (3), rest (3), them (3), system (3), units (3), simple (3), jefimenko (3), infinitely (3), conducting (3), infinitesimal (3), plane (3), absence (3), hence (3), opposite (3), outside (3), common (3), considered (3), advanced (3), solutions (3), another (3), set (3), caused (3), acceleration (3), term (3), larmor (3), arbitrarily (3), potentials (3), satisfy (3), velocity (3), divided (3), cdot (3), liénard (3), wiechert (3), disturbances (3), begin (3), will (3), laws (3), symmetry (3), spaced (3), experienced (3), order (3), constitutive (3), relation (3), extend (3), still (3), polarization (3), coupled (3), expression (3), permeability (3), describe (3), derivative (3), change (3), number (3), useful (3), changes (3), must (3), complex (3), electrical (3), way (3), because (3), sign (3), delta (3), illustration (3), inverse (3), conservative (3), newton (3), small (3), discrete (3), electrons (3), helmholtz (3), dots (3), meter (3), directed (3), fur (3), circuit (3), tools (3), 100 (2), languages (2), table (2), contact (2), about (2), privacy (2), policy (2), under (2), you (2), use (2), was (2), october (2), 2026 (2), categories (2), wayback (2), missing (2), publisher (2), errors (2), date (2), march (2), short (2), united (2), machine (2), archived (2), lectures (2), has (2), michael (2), 107 (2), 01402 (2), 471 (2), 2017 (2), 108 (2), 42041 (2), 01297 (2), 251 (2), spacetime (2), 4899 (2), inhomogeneous (2), medium (2), vol (2), arnold (2), sons (2), 470 (2), original (2), attract (2), product (2), inversely (2), closed (2), applications (2), 1970 (2), longman (2), addison (2), wesley (2), 201 (2), 305 (2), 055005 (2), references (2), conductive (2), close (2), having (2), indicate (2), moment (2), ring (2), inside (2), figure (2), formulas (2), interpretation (2), unphysical (2), but (2), slower (2), accelerating (2), known (2), derived (2), pointing (2), gamma (2), cause (2), events (2), does (2), travel (2), faster (2), found (2), considering (2), revert (2), outwards (2), continue (2), never (2), disturbance (2), speeds (2), travelling (2), generated (2), boundary (2), systems (2), calculation (2), reference (2), evidence (2), transformation (2), observed (2), theta (2), sin (2), linearity (2), dependence (2), throughout (2), constant (2), matter (2), three (2), induced (2), convenient (2), definitive (2), stored (2), int (2), contributions (2), associated (2), respect (2), contribute (2), addition (2), behavior (2), instance (2), defines (2), vacuum (2), infinity (2), end (2), further (2), cannot (2), induces (2), nearby (2), curved (2), objects (2), areas (2), blue (2), red (2), approximated (2), planes (2), experience (2), plate (2), capacitor (2), obey (2), mass (2), similar (2), parallels (2), present (2), surrounding (2), many (2), best (2), representation (2), follow (2), allows (2), distributions (2), created (2), says (2), aligned (2), base (2), indicating (2), signs (2), cat (2), causes (2), molecules (2), styrofoam (2), descriptions (2), nature (2), study (2), whose (2), concept (2), drawn (2), important (2), originate (2), strength (2), acts (2), varies (2), 469 (2), exerted (2), atoms (2), atomic (2), exert (2), attractive (2), object (2), weaker (2), stronger (2), savart (2), poynting (2), ohm (2), lenz (2), kirchhoff (2), joule (2), biot (2), reluctance (2), network (2), theorem (2), sheet (2), appearance (2), upload (2), file (2), read (2), english (2), norsk (2), bahasa (2), беларуская (2), log (2), create (2), account (2), donate (2), menu (2), add, topic, mobile, cookie, statement, statistics, developers, code, conduct, legal, safety, contacts, disclaimers, available, additional, apply, site, agree, registered, trademark, profit, organization, foundation, inc, creative, attribution, sharealike, license, rendered, parsoid, last, edited, utc, hidden, webarchive, template, category, periodical, permanently, 2024, different, quantities, https, org, index, php, title, electric_field, oldid, 1379298894, yale, lux, israel, czech, republic, bnf, data, france, national, gnd, authority, control, databases, chapter, online, textbook, 2010, chapters, rochester, frank, wolfs, georgia, hyperphysics, nave, browne, mcgraw, hill, schaum, 161399, science, jackson, 665, 38073290, 30932, 664, 4th, kingdom, 454, 1021068059, third, 255, 1105718330, naber, gregory, 2012, springer, 804823303, 4419, 7837, geometry, minkowski, mathematics, oliver, rosser, 1968, 6258, 1007, 6559, via, website, 2022, 1017, cbo9781139012973, 241, incompatibility, 1963, pergamon, 285, ordinates, 7581, 6499, course, theoretical, lifshitz, evgeny, landau, lev, davidovich, bennet, 1974, 7131, 2459, modern, grant, phillips, 2008, 92712, 357, 0134813677, salam, abdus, december, 1976, 652, scientist, quarks, leptons, come, out, play, huray, paul, 2009, ieee, 205, 54276, gwrowe, 2019, 2020, november, physicspages, com, 50355, 356, through, equals, enclosed, upper, saddle, river, prentice, hall, 40251748, 805326, tou, stephen, 97846, visualization, morely, hughes, 5th, 582, 42629, principles, umashankar, korada, 1989, world, scientific, 9971, 0921, sears, francis, 1982, 6th, 07199, 9th, bureau, weights, measures, jun, 822, 2272, serway, raymond, vuille, chris, 2014, 10th, cengage, learning, 533, 14282, 532, college, richard, 02115, roche, 2016, introducing, 125014664, s2cid, 1088, 0031, 9120, 2016phyed, 51e5005r, bibcode, education, paper, analog, computer, modelling, teledeltos, teltron, tube, summary, relations, equilibrium, formed, scale, resembles, exhibit, equatorial, sqrt, disc, long, cylindrical, large, wire, configuration, although, consistent, well, limit, corrected, quantum, mechanical, indicates, governed, future, neglected, been, theories, exploring, wheeler, absorber, exist, yet, instead, uniqueness, valid, dependent, correction, obtained, lorenz, gauge, needs, accounted, expressed, contribution, originated, corresponding, factor, dot, imposes, requires, like, separated, confirm, provides, coming, abrupt, stop, immediately, classically, stopping, around, expected, propagates, radially, towards, assumed, range, restricted, makes, impossible, construct, violates, technical, difficulty, supports, longer, unique, connects, radiates, possible, radiating, pulse, gaussian, virtual, causal, efficacy, locality, paradox, reduces, satisfied, breaking, problem, specification, illustrate, unequally, radial, appear, equally, invariance, derive, invariant, supported, experimental, alternatively, assigning, definition, following, applicable, involved, arguments, solving, manner, ratio, angle, extents, homogeneity, isotropy, anisotropic, isotropic, homogeneous, presence, helpful, notion, separately, clear, effectively, applied, dipoles, serves, simplification, simplified, moments, list, misleading, split, particular, transforms, relatively, accordingly, decomposing, specific, exists, vectors, intricately, multi, dimensional, differential, solved, combined, produce, accordance, along, circuital, approximately, takes, perfectly, nevertheless, diagrams, illustrating, how, intersect, loops, diagram, made, surfaces, plot, works, even, intersecting, span, plotted, correctly, metal, arrows, every, placing, maintaining, approximation, near, edge, distorted, assuming, separating, arises, positively, increases, micro, nano, semiconductors, typical, achieved, applying, apart, finite, size, middle, edges, very, nearly, central, suggests, similarities, universal, gravitation, gravitoelectromagnetism, unchanging, fully, located, mathematically, dimensions, conversely, dirac, some, models, sources, section, recovered, taking, justifies, posteriori, previous, independently, gradient, then, analogous, irrotational, decomposition, ell, iint, summing, increments, iiint, integrating, calculated, collection, individual, calculating, multiple, gives, except, itself, becomes, seen, everywhere, toward, decreases, valued, note, replaced, empty, unlike, make, easy, calculate, leaving, depends, disappears, taken, equivalent, exerts, inductive, steady, clinging, build, motions, slight, attraction, plastic, pieces, clothes, cling, triboelectric, peanuts, enough, relationship, stating, therefore, implies, kinds, arising, simpler, treatment, generally, treated, unified, 307, 327, visualized, those, introduced, property, represents, amount, several, properties, including, always, terminate, enter, good, angles, cross, themselves, representative, actually, permeates, intervening, more, fewer, depending, precision, desired, 479, follows, basis, means, were, doubled, double, twice, quarter, masses, infinitesimally, associates, exploited, technology, holds, responsible, results, chemical, bonding, nucleus, chemistry, surrounds, electrically, single, group, capacity, repulsive, being, mutually, take, place, informally, nearer, manifestations, fundamental, interactions, weber, volta, thomson, tesla, steinmetz, singer, ritchie, poisson, ørsted, neumann, kelvin, hopkinson, hertz, henry, green, gilbert, gibbs, galvani, franklin, fizeau, fitzgerald, einstein, davy, arago, scientists, bremsstrahlung, synchrotron, stress, covariant, transformer, stator, rotor, real, permeance, magnetomotive, gyrator, london, waveguides, watt, series, resonant, cavities, resistance, analysis, heating, inductance, impedance, electromotive, electrolysis, power, direct, capacitance, alternating, abraham, eddy, cyclotron, hand, rule, magnetization, scalar, magnetostatics, triboelectricity, insulator, discharge, electret, conductor, phenomena, textbooks, computational, optics, dimension, symbols, suspended, depicted, shown, redirects, australian, band, encyclopedia, item, wikiversity, wikibooks, projects, printable, version, download, print, export, switch, legacy, parser, get, shortened, url, information, what, actions, talk, isizulu, 閩南語, bân, lâm, wolof, winaray, tiếng, việt, oʻzbekcha, ўзбекча, اردو, українська, татарча, tatarça, türkçe, tagalog, ไทย, తెలుగు, தமிழ், svenska, sunda, српски, srpski, shqip, chishona, slovenščina, slovenčina, srpskohrvatski, српскохрватски, sicilianu, русский, română, português, پښتو, پنجابی, piemontèis, polski, ਪੰਜਾਬੀ, ଓଡ଼ିଆ, occitan, bokmål, nynorsk, nederlands, مازِرونی, မြန်မာဘာသာ, melayu, मराठी, монгол, മലയാളം, македонски, मगही, latviešu, lietuvių, limburgs, latina, 한국어, ಕನ್ನಡ, ភាសាខ្មែរ, қазақша, ქართული, 日本語, italiano, íslenska, ido, indonesia, հայերեն, magyar, kreyòl, ayisyen, hrvatski, हिन्दी, עברית, galego, gaeilge, nordfriisk, français, suomi, فارسی, estremeñu, euskara, eesti, español, esperanto, ελληνικά, deutsch, dansk, чӑвашла, čeština, کوردی, català, bosanski, বাংলা, भोजपुरी, български, тарашкевіца, تۆرکجه, azərbaycanca, asturianu, অসমীয়া, العربية, አማርኛ, alemannisch, top, personal, pages, recent, community, portal, learn, random, navigation, jump, content,

Text of the page (random words):
perty that when drawn so that each line represents the same amount of flux the strength of the field is proportional to the density of the lines 9 field lines due to stationary charges have several important properties including that they always originate from positive charges and terminate at negative charges they enter all good conductors at right angles and they never cross or close in on themselves 6 479 the field lines are a representative concept the field actually permeates all the intervening space between the lines more or fewer lines may be drawn depending on the precision to which it is desired to represent the field 8 the study of electric fields created by stationary charges is called electrostatics faraday s law describes the relationship between a time varying magnetic field and the electric field one way of stating faraday s law is that the curl of the electric field is equal to the negative time derivative of the magnetic field 10 327 in the absence of time varying magnetic field the electric field is therefore called conservative i e curl free 10 24 90 91 this implies there are two kinds of electric fields electrostatic fields and fields arising from time varying magnetic fields 10 305 307 while the curl free nature of the static electric field allows for a simpler treatment using electrostatics time varying magnetic fields are generally treated as a component of a unified electromagnetic field the study of magnetic and electric fields that change over time is called electrodynamics mathematical formulation edit main article mathematical descriptions of the electromagnetic field electric fields are caused by electric charges described by gauss s law 11 and time varying magnetic fields described by faraday s law of induction 12 together these laws are enough to define the behavior of the electric field however since the magnetic field is described as a function of electric field the equations of both fields are coupled and together form maxwell s equations that describe both fields as a function of charges and currents evidence of an electric field styrofoam peanuts clinging to a cat s fur due to static electricity the triboelectric effect causes an electrostatic charge to build up on the fur due to the cat s motions the electric field of the charge causes polarization of the molecules of the styrofoam due to electrostatic induction resulting in a slight attraction of the light plastic pieces to the charged fur this effect is also the cause of static cling in clothes electrostatics edit main article coulomb s law in the special case of a steady state stationary charges and currents the maxwell faraday inductive effect disappears the resulting two equations gauss s law e ρ ε 0 displaystyle nabla cdot mathbf e frac rho varepsilon _ 0 and faraday s law with no induction term e 0 displaystyle nabla times mathbf e 0 taken together are equivalent to coulomb s law which states that a particle with electric charge q 1 displaystyle q_ 1 at position r 1 displaystyle mathbf r _ 1 exerts a force on a particle with charge q 0 displaystyle q_ 0 at position r 0 displaystyle mathbf r _ 0 of 13 f 01 q 1 q 0 4 π ε 0 r 01 r 01 2 q 1 q 0 4 π ε 0 r 01 r 01 3 displaystyle mathbf f _ 01 frac q_ 1 q_ 0 4 pi varepsilon _ 0 hat mathbf r _ 01 over mathbf r _ 01 2 frac q_ 1 q_ 0 4 pi varepsilon _ 0 mathbf r _ 01 over mathbf r _ 01 3 where f 01 displaystyle mathbf f _ 01 is the force on charged particle q 0 displaystyle q_ 0 caused by charged particle q 1 displaystyle q_ 1 ε 0 is the permittivity of free space r 01 displaystyle hat mathbf r _ 01 is a unit vector directed from r 1 displaystyle mathbf r _ 1 to r 0 displaystyle mathbf r _ 0 r 01 displaystyle mathbf r _ 01 is the displacement vector from r 1 displaystyle mathbf r _ 1 to r 0 displaystyle mathbf r _ 0 note that ε 0 displaystyle varepsilon _ 0 must be replaced with ε displaystyle varepsilon permittivity when charges are in non empty media when the charges q 0 displaystyle q_ 0 and q 1 displaystyle q_ 1 have the same sign this force is positive directed away from the other charge indicating the particles repel each other when the charges have unlike signs the force is negative indicating the particles attract to make it easy to calculate the coulomb force on any charge at position r 0 displaystyle mathbf r _ 0 this expression can be divided by q 0 displaystyle q_ 0 leaving an expression that only depends on the other charge the source charge 14 4 e 1 r 0 f 01 q 0 q 1 4 π ε 0 r 01 r 01 2 q 1 4 π ε 0 r 01 r 01 3 displaystyle mathbf e _ 1 mathbf r _ 0 frac mathbf f _ 01 q_ 0 frac q_ 1 4 pi varepsilon _ 0 hat mathbf r _ 01 over mathbf r _ 01 2 frac q_ 1 4 pi varepsilon _ 0 mathbf r _ 01 over mathbf r _ 01 3 where e 1 r 0 displaystyle mathbf e _ 1 mathbf r _ 0 is the component of the electric field at q 0 displaystyle q_ 0 due to q 1 displaystyle q_ 1 this is the electric field at point r 0 displaystyle mathbf r _ 0 due to the point charge q 1 displaystyle q_ 1 it is a vector valued function equal to the coulomb force per unit charge that a positive point charge would experience at the position r 0 displaystyle mathbf r _ 0 since this formula gives the electric field magnitude and direction at any point r 0 displaystyle mathbf r _ 0 in space except at the location of the charge itself r 1 displaystyle mathbf r _ 1 where it becomes infinite it defines a vector field from the above formula it can be seen that the electric field due to a point charge is everywhere directed away from the charge if it is positive and toward the charge if it is negative and its magnitude decreases with the inverse square of the distance from the charge the coulomb force on a charge of magnitude q displaystyle q at any point in space is equal to the product of the charge and the electric field at that point f q e displaystyle mathbf f q mathbf e the si unit of the electric field is the newton per coulomb n c or volt per meter v m in terms of the si base units it is kg m s 3 a 1 superposition principle edit due to the linearity of maxwell s equations electric fields satisfy the superposition principle which states that the total electric field at a point due to a collection of charges is equal to the vector sum of the electric fields at that point due to the individual charges 4 this principle is useful in calculating the field created by multiple point charges if charges q 1 q 2 q n displaystyle q_ 1 q_ 2 dots q_ n are stationary in space at points r 1 r 2 r n displaystyle mathbf r _ 1 mathbf r _ 2 dots mathbf r _ n in the absence of currents the superposition principle says that the resulting field is the sum of fields generated by each particle as described by coulomb s law e r e 1 r e 2 r e n r 1 4 π ε 0 i 1 n q i r i r i 2 1 4 π ε 0 i 1 n q i r i r i 3 displaystyle begin aligned mathbf e mathbf r mathbf e _ 1 mathbf r mathbf e _ 2 mathbf r dots mathbf e _ n mathbf r 1 over 4 pi varepsilon _ 0 sum _ i 1 n q_ i hat mathbf r _ i over mathbf r _ i 2 1 over 4 pi varepsilon _ 0 sum _ i 1 n q_ i mathbf r _ i over mathbf r _ i 3 end aligned where r i displaystyle hat mathbf r _ i is the unit vector in the direction from point r i displaystyle mathbf r _ i to point r displaystyle mathbf r r i displaystyle mathbf r _ i is the displacement vector from point r i displaystyle mathbf r _ i to point r displaystyle mathbf r continuous charge distributions edit the superposition principle allows for the calculation of the electric field due to a distribution of charge density ρ r displaystyle rho mathbf r by considering the charge ρ r d v displaystyle rho mathbf r dv in each small volume of space d v displaystyle dv at point r displaystyle mathbf r as a point charge the resulting electric field d e r displaystyle d mathbf e mathbf r at point r displaystyle mathbf r can be calculated as d e r ρ r 4 π ε 0 r r 2 d v ρ r 4 π ε 0 r r 3 d v displaystyle d mathbf e mathbf r frac rho mathbf r 4 pi varepsilon _ 0 hat mathbf r over mathbf r 2 dv frac rho mathbf r 4 pi varepsilon _ 0 mathbf r over mathbf r 3 dv where r displaystyle hat mathbf r is the unit vector pointing from r displaystyle mathbf r to r displaystyle mathbf r r displaystyle mathbf r is the displacement vector from r displaystyle mathbf r to r displaystyle mathbf r the total field is found by summing the contributions from all the increments of volume by integrating the charge density over the volume v displaystyle v e r 1 4 π ε 0 v ρ r r r 3 d v displaystyle mathbf e mathbf r frac 1 4 pi varepsilon _ 0 iiint _ v rho mathbf r mathbf r over mathbf r 3 dv similar equations follow for a surface charge with surface charge density σ r displaystyle sigma mathbf r on surface s displaystyle s e r 1 4 π ε 0 s σ r r r 3 d a displaystyle mathbf e mathbf r frac 1 4 pi varepsilon _ 0 iint _ s sigma mathbf r mathbf r over mathbf r 3 da and for line charges with linear charge density λ r displaystyle lambda mathbf r on line l displaystyle l e r 1 4 π ε 0 l λ r r r 3 d ℓ displaystyle mathbf e mathbf r frac 1 4 pi varepsilon _ 0 int _ l lambda mathbf r mathbf r over mathbf r 3 d ell electric potential edit main article electric potential see also helmholtz decomposition and conservative vector field irrotational vector fields if a system is static such that magnetic fields are not time varying then by faraday s law the electric field is curl free in this case one can define an electric potential that is a function φ displaystyle varphi such that e φ displaystyle mathbf e nabla varphi 15 this is analogous to the gravitational potential the difference between the electric potential at two points in space is called the potential difference or voltage between the two points in general however the electric field cannot be described independently of the magnetic field given the magnetic vector potential a defined so that b a displaystyle mathbf b nabla times mathbf a one can still define an electric potential φ displaystyle varphi such that e φ a t displaystyle mathbf e nabla varphi frac partial mathbf a partial t where φ displaystyle nabla varphi is the gradient of the electric potential and a t displaystyle frac partial mathbf a partial t is the partial derivative of a with respect to time faraday s law of induction can be recovered by taking the curl of that equation 16 e a t b t displaystyle nabla times mathbf e frac partial nabla times mathbf a partial t frac partial mathbf b partial t which justifies a posteriori the previous form for e continuous vs discrete charge representation edit main article charge density the equations of electromagnetism are best described in a continuous description however charges are sometimes best described as discrete points for example some models may describe electrons as point sources where charge density is infinite on an infinitesimal section of space a charge q displaystyle q located at r 0 displaystyle mathbf r _ 0 can be described mathematically as a charge density ρ r q δ r r 0 displaystyle rho mathbf r q delta mathbf r mathbf r _ 0 where the dirac delta function in three dimensions is used conversely a charge distribution can be approximated by many small point charges electrostatic fields edit main article electrostatics illustration of the electric field surrounding a positive red and a negative blue charge electrostatic fields are electric fields that do not change with time such fields are present when systems of charged matter are stationary or when electric currents are unchanging in that case coulomb s law fully describes the field 17 parallels between electrostatic and gravitational fields edit see also gravitoelectromagnetism coulomb s law which describes the interaction of electric charges f q q 4 π ε 0 r r 2 q e displaystyle mathbf f q left frac q 4 pi varepsilon _ 0 frac mathbf hat r mathbf r 2 right q mathbf e is similar to newton s law of universal gravitation f m g m r r 2 m g displaystyle mathbf f m left gm frac mathbf hat r mathbf r 2 right m mathbf g where r r r textstyle mathbf hat r mathbf frac r r this suggests similarities between the electric field e and the gravitational field g or their associated potentials mass is sometimes called gravitational charge 18 electrostatic and gravitational forces both are central conservative and obey an inverse square law uniform fields edit illustration of the electric field between two parallel conductive plates of finite size known as a parallel plate capacitor in the middle of the plates far from any edges the electric field is very nearly uniform a uniform field is one in which the electric field is constant at every point it can be approximated by placing two conducting plates parallel to each other and maintaining a voltage potential difference between them it is only an approximation because of boundary effects near the edge of the planes the electric field is distorted because the plane does not continue assuming infinite planes the magnitude of the electric field e is e δ v d displaystyle e frac delta v d where δ v is the potential difference between the plates and d is the distance separating the plates the negative sign arises as positive charges repel so a positive charge will experience a force away from the positively charged plate in the opposite direction to that in which the voltage increases in micro and nano applications for instance in relation to semiconductors a typical magnitude of an electric field is in the order of 10 6 v m 1 achieved by applying a voltage of the order of 1 volt between conductors spaced 1 μm apart electric field lines edit the electric field lines with arrows of a charge induces surface charges red and blue areas on metal objects due to electrostatic induction main article field line a convenient way to plot the electric field that works even for complex electric fields is to use field lines 19 here the magnitude and direction of an electric field in a region is represented by a number of non intersecting curved lines that span the region if plotted correctly the direction of the electric field at any given point is represented by the direction of nearby lines while the magnitude is represented by the density of the field lines in that region electric field lines do not intersect they begin at positive charge or extend from infinity and end at negative charge or extend to infinity further the number of field lines from a given charge must be proportional to that charge electrostatic fields cannot form closed loops see the figure for an example of a complex electric field line diagram made for a positive point charge which induces electrical charge on the surfaces of 3 nearby conductors field lines can only approximately represent the electric field in a given region it takes an infinite number of field lines to represent the electric field perfectly nevertheless these diagrams are useful at illustrating how the electric field changes over a given region electromagnetic fields edit main article electromagnetic field electroma...