Electric force is attraction or repulsion between electric charges. Magnetism is moving-charge relativistic effects and so is apparent electric force {electromagnetism}|. If electric fields cancel, because positive and electric charges are equal, magnetic fields do not necessarily cancel, because both positive and electric charges can move relativistically.
Particle properties {charge, electricity}| can cause electric force. Electron charge {negative charge} is one negative unit. Proton charge {positive charge} is one positive unit. Total electric charge is sum of particle electric charges.
static electricity
Rubbing glass with cloth keeps protons on glass and puts electrons on cloth. Rubbing rubber with cloth puts electrons on rubber and keeps protons on cloth. Rubbing energy frees electrons from rubbed material surface. Quickly pulling the materials apart leaves net charge on both materials. Sliding on rugs rubs electrons off rug, and touching metal doorknobs makes electrons jump to metal.
static electricity: lightning
High winds, when hot air rises, rub higher cold air, separate electrons from air molecules, and take electrons away before they can recombine. Lightning carries electrons back to positive-charge regions or to ground.
strong nuclear force
Only strong nuclear force can change particle electric charge.
Surface voltages can move charges around semiconductors {charge coupling}|. Semiconductors have capacitance. Charge moves between capacitors at each clock pulse. Solid-state TV cameras and memory circuits use charge coupling. Semiconductors {charge coupled device} (CCD) can move free electric charges from one storage element to another, by externally changing voltage. Charge can vary by varying voltage and capacitance. Image sensors and computer memories use CCDs.
Electric forces on materials can pull electrons in one direction and protons in opposite direction {induction, charge} {charge induction}|.
dielectric
Conductors have free charges, so charges move to counter outside electric force, with no net charge. Dielectrics have no free charges, so induction pulls electrons and protons apart to make induced charge and dipoles.
factors
If electric field is more, electric force is more, and system has more dipoles. If atoms are small, smaller mass moves easier, and system has more dipoles.
factors: temperature
In polar materials, if temperature is lower, material has fewer random motions, and material has more dipoles. In non-polar materials, temperature has little effect.
factors: frequency
If electric-field frequency is more than 10^10 Hz, dipole moments cancel, because dipole moments change slower than field changes. If electric-field frequency is above 10^11 Hz, bending and stretching dipole moments cancel, because vibrations are slower than frequency, and only electrons affect polarization.
examples
Sifting sugar or streaming water through electric fields illustrates charge induction.
Outside electric force on dielectrics can pull electrons one way and protons opposite way, to separate charges {dipole}|. Negative charges are at one end, and positive charges are at other end, along outside-electric-field direction.
Instruments {electroscope}| can detect static electricity.
Friction can cause glow {St. Elmo's fire}| around objects in storms.
Objects can have stationary extra surface charges {static electricity}|. Electric charge is on material surface, because electrons repel each other to farthest points. More charges are at higher-curvature surface points, because repulsions are less where average distances are more. Sparks, van de Graaf generators, pith balls, cloths and rods, and electroscopes demonstrate static electricity.
Ions can have charge {valence, ion}, of -7 to +7.
Electric force depends on charge and distance {Coulomb's law} {Coulomb law}. Electric force F between two charges varies directly with charge q and varies inversely with square of distance r between charges: F = k * q1 * q2 / r^2 = (1 / (4 * pi * e)) * q1 * q2 / r^2.
permittivity
Electric-force constant k depends on medium electric permittivity e: k = 1 / (4 * pi * e).
distance
Force varies with distance squared, because space is isotropic in all directions, time has no effect, and field-line number stays constant as surface area increases. Sphere surface area = 4 * pi * r^2.
charge
Force depends on both charges, because force is interaction. Electric force depends on charge linearly, because charge directly causes force. Because charges can be positive or negative, electric force can be attractive positive or repulsive negative. If both charges are positive or negative, electric force is positive. If one charge is positive and one charge is negative, electric force is negative.
comparison
Electric force is very strong compared to gravity. Gravitational force and electric force equations are similar, because interactions cause both forces and both forces radiate in all directions.
voltage
dW = F * ds = q * dV. F = q * dV / ds = q * E.
In potential equations {d'Alembert equation, electromagnetism} for electric and magnetic fields, source-charge density and three current-density components make four potentials for each field.
For stationary magnet and moving wire in a circuit, electric force F makes electric current, and force varies directly with magnetic-flux (phi, depending on magnetic field B and surface area A) change over time {Faraday law of induction} {Faraday's law of induction}: F ~ d(phi)/dt, and phi = sum over A of B. Induced electric current makes magnetic field opposed to stationary magnetic field. For moving magnet and stationary wire, electric field E makes electric current in wire, and electromotive force on charges varies directly with magnetic-flux change over time. Faraday law of induction applies to both Maxwell-Faraday equation, for changing magnetic field and stationary charge, and Lorentz force law, for stationary magnet and moving wire in a circuit.
A constant {fine-structure constant} {coupling constant} measures electromagnetism force strength (Sommerfield) [1916]. It has no dimensions. It equals 7.297 * 10^-3 ~ 1/137. The fine-structure constant depends on electron charge, Planck constant, light speed, and permittivity or permeability or Coulomb constant. The coupling constant measures photon-electron force.
For changing magnetic field and stationary charge, changing magnetic field B makes electric field E {Maxwell-Faraday equation} {Faraday's law}: curl of E = partial derivative over time of B. This has an integral form {Kelvin-Stokes theorem}: line integral of E = integral over surface area of partial derivative of B with time.
For stationary magnet and moving wire in a circuit, Lorentz force F on charges makes electric current and electric force varies directly with electric charge q and with wire velocity v and magnetic field B cross product {Lorentz force law}: F ~ q * (v x B). Induced electric current makes magnetic field opposed to stationary magnetic field.
Flux equals integral of electric field E over area A, which equals sum of charges q divided by electric permittivity e {Gauss' law} {Gauss law}: integral of E * dA = (sum of q) / e. Gauss' law can find electric field and voltage.
Divergence of magnetic field B equals zero {Gauss law of magnetism} {Gauss's law of magnetism} {transversality requirement} {absence of free magnetic poles}: divergence of B = 0, or line integral over a surface of B = 0. Magnetic fields are solenoids. Magnetic "charges" are dipoles, and there are no magnetic monopoles.
Electric fields are like force lines {force lines} {lines of force}| radiating from center outward in all directions. Force lines per area equal electric field. Force lines have direction, from positive to negative, because test charges are positive. Force lines entering closed surfaces are negative. Force lines leaving closed surfaces are positive. For large charged objects, electric-field lines are perpendicular to surfaces, because force lines are symmetric around surface perpendiculars.
Electric-force lines pass through areas in directions {flux, electric} {electric flux}. Positive and negative fluxes from different sources add together. Does infinite flux exist? Perhaps, field lines cannot come closer than Planck length. Then flux has maximum density, and field has no infinities.
For electricity, energy W {electric energy}| is charge q times voltage V: W = q*V. Electric energy is in joules: W = F*s = (k * q * Q / s^2) * s = q * (k * Q / s) = q * (E / s) = q*V, where F is electric force, k is electric-force constant, Q is charge, E is electric field, and s is distance.
Electric charge causes potential energy {electric field}| that radiates in all directions. Electric fields can cancel each other, because charges can be positive or negative.
potential
Electric charges q Q make electric force F, which decreases with distance r squared: F = k * q * Q / r^2, where k is electric force constant. Electric-field strength intensity H changes with distance r from charge Q: H = F/q = k * Q / r^2, where k is electric-force constant. Electric field depends on material electric permittivity.
Different distances have different potential energies. Charge can move between two electric-field points, causing potential-energy-change potential difference. Electric-field energy change E is potential difference V times charge q: E = F*s = (k * q * Q / s^2) * s = q * (k * Q / s) = q*V. Potential-energy difference is work done by electric force as charge moves through distance.
examples: surface
Potential is equal all over large charged-object surfaces. Otherwise, electrons flow to lowest-potential location to equalize potential.
examples: plate
Electric field H above charged plates equals charge q divided by electric permittivity k: H = q/k.
examples: rod
Electric field H above long rods varies as reciprocal of distance d from rod: H = C * (1/d).
examples: point
Electric field H around point charges or spheres varies as reciprocal of square of distance r from center: H = k * Q / r^2.
examples: dipole
Electric field H around dipole varies as reciprocal of cube of distance d from dipole center: H = C * (1 / d^3).
For electricity, power P {electric power}| is current I times voltage V: P = dE / dt = V * dq / dt = V*I.
Pressure on crystals can cause voltage {piezoelectricity}|. Pressure polarizes crystals, such as quartz, mica, or lead zirconate titanate (PZT). Pressure changes polarized-material charge separation to make voltage. In reverse, applying electric field contracts crystals in field direction.
Tendency for charges to flow depends on electric energy per charge {voltage}| {potential difference}. Higher potential is positive and attracts negative charge. If two points have potential difference and path exists, charge flows from one point to the other.
energy
Because field is electric force F divided by charge q, voltage V is electric field H times distance ds moved in field direction: V = H * ds = (F/q) * ds = (F * ds) / q = W/q, where W is electric energy. Voltage is electric energy divided by charge.
field
Separating charges using work creates electric field, with voltage between charges. Batteries separate charges to create voltage. Electromagnetic induction creates voltage by separating charges. Voltage V equals area A times negative of field change dH divided by time change dt: V = A * -dH / dt. Voltage V equals negative of inductance I times current change di divided by time change dt: V = -I * di / dt.
Electric fields {wakefield} can pulse and so force electrons to accelerate.
Moving-electron and stationary-molecule interactions oppose electric current flow {resistance}| and turn electric energy into heat. Electrical resistance depends on path length, cross-sectional area, and material resistivity.
voltage
Resistance makes heat from electrical kinetic energy and, as potential energy decreases, drops potential across resistor.
current
For same voltage, more resistance makes less current, because flow slows.
factors
Resistance is more for poor conductors with few electrons that can move, for longer conductor length, or for less cross-sectional area. If cross-sectional area is more, conductor perimeter is more, fewer electron collisions happen, and resistance is less. If conductor length is more, distance is longer, and total resistance is more. If material resistivity is more, conductor has fewer free charges, and resistance is more.
factors: temperature
In conductors at higher temperature, resistance is more, because random motions are more. In insulators or semiconductors at higher temperature, resistance is less, because more electrons are free to move. Alloys have smaller resistance change when temperature changes, because alloys have fewer free electrons than pure metals.
resistor
Electrical devices {resistor} can have resistance. Conductor resistance R equals material resistivity r, which differs at different temperatures, times conductor length l divided by conductor cross-sectional area A: R = r * l / A.
resistivity
Resistivity is 10^-6 to 10^-1 ohm-cm for conductors, 10^-1 to 10^8 ohm-cm for semiconductors, and 10^8 to 10^21 ohm-cm for insulators.
examples
Resistance in incandescent light bulbs creates light. Resistance in electric heaters creates heat. Fuses, circuit breakers, voltmeters, ammeters, tube resistors, rod resistors, and coil resistors demonstrate electrical resistance. Lie detectors detect skin electrical resistance, which varies with sweat amount.
Resistance reciprocal {conductance}| measures current-flow ease.
At same temperature, electrical-conductivity to heat-conductivity ratio is the same for all metals {law of Wiedemann and Franz} {Wiedemann and Franz law}.
Materials {conductor}|, such as metals, can allow electrons to move almost freely.
dipoles
Because electrons are free to move, no dipoles form. Conductor dielectric strength is zero, and dielectric constant is infinite, because charges can move freely. Rubbing metal with cloth cannot rub off charges, because electrons move freely and quickly in conductors.
spark
If charge touches conductors, electrons flow to neutralize charge, typically making sparks.
spread
Potential difference between conductor points is zero, because all electrons already repel each other equally. No electrons flow.
compression
Compressing metal increases conductivity, because crystals have fewer imperfections.
Materials can allow electrons to move almost freely {conduction, electricity}|. Semiconductors allow electrons to move with high resistance. Insulators do not conduct electricity. Circuit loads are either conductors or semiconductors.
Electric force causes average drift velocity per unit force {mobility, charge} {charge mobility, conductor}|.
Metallic bonds are electron deficient and leave electrons free {free electron}. Metal has electrons that can move among atoms around metal surface. Outside electric force can pull electrons completely away from atoms.
In conductors, moving electrons have average time between collisions {mean free time}| and have average distance, mean free path, between collisions. Collisions tend to reduce charge velocities.
In conductors, voltage V equals resistance R times current I {Ohm's law} {Ohm law}: V = R*I.
Most materials {insulator}| {dielectric} allow no free electron movement. Air, vacuum, paper, and glass are insulators.
dipoles
Outside electric field separates electrons and protons, to make induced charge. Inducing charge can be easy or hard. Dielectric strength is ratio between material capacitance and vacuum capacitance. For vacuum, dielectric constant is 1. For insulators, dielectric constant is 1 to 8. For water, dielectric constant is 81, because water has high polarization and free dipole rotation. For conductors, dielectric constant is infinite. Lustrous metals have negative dielectric constant.
Materials have ease by which electric fields can go through {permittivity}|. Metals have free electrons and cannot have electric fields inside. Insulators have charges that move relative to electric field and oppose electric field. Empty space has no charges and allows electric field. Electric-force constant k inversely depends on permittivity.
Insulators have different abilities to make dipoles {polarizability}| {polarization, electricity}. If polarization is more, refraction index is more. Polarization K is refractive index n squared: K = n^2. Metal has free electrons and cannot make dipoles. Empty space has no charges and cannot make dipoles.
Materials {semiconductor}| can have electrons that can move from atom to atom in atomic-orbital conducting bands. Silicon and germanium are semiconductors. Semiconductor compounds include indium gallium arsenide and indium antimonide.
impurities
Semiconductors can be silicon with added gallium {P-type semiconductor} or arsenic {N-type semiconductor}. P-type semiconductors transfer electron vacancies. N-type semiconductors transfer electrons. Holes and electrons must move in opposite directions to complete circuit.
electric charge
If charge touches semiconductor, no change happens, because semiconductor electrons are not free to move.
Impurities {doping}| added to silicon or germanium supply more negative or positive charges, to make more conduction.
donor
Adding material with five electrons in highest orbital {donor impurity} adds extra electron. Antimony, arsenic, and phosphorus are donors {n-type semiconductor}.
acceptor
Adding material that has three electrons in highest orbital {acceptor impurity} results in extra proton {electron deficiency}. Gallium, indium, aluminum, and boron are acceptors {p-type semiconductor}.
junction
If p-type semiconductor touches n-type semiconductor, electrons in n-type semiconductor flow into holes in p-type semiconductor until reaching balance, with voltage across junction. p-type semiconductor has become slightly negative. n-type semiconductor has become slightly positive. No more free charges exist. Junction width is 50 atoms.
diode
If voltage across np junction makes p side positive, current flows greatly, because p side attracts electrons. If voltage across np junction makes p side negative, no current flows, because p side repels electrons. np junctions allow current in only one direction and allow current to be ON or zero OFF, like diodes.
Semiconductors can emit light {electroluminescence}| across pn junctions when current flows. Phosphors can glow if AC current passes through. Machine sprays glass panel with thin transparent metal layer, adds a phosphor layer, and adds thin metal foil. Electroluminescence is efficient and cool but allows only low light levels.
One electron and one hole {exciton} can bind electrostatically for 4 to 40 microseconds, 1150 nanometers apart. Electric forces cause free electrons and holes to drift in opposite directions, at same velocity. Electric force causes average drift velocity per unit force {charge mobility, exciton}. When electron meets hole, they merge. At constant force, ejections and recombinations are in equilibrium.
A thin layer of electrons is between two semiconductors. Near 0 K in high magnetic field [1982], pairs {quasiparticle, pair} of excited superposition of electron states have fractional charges {fractional quantum Hall effect}, with edge effects {edge state}. Fractional quantum Hall effect can extend to four dimensions, as on five-dimensional-sphere surfaces, which have three-dimensional edge states that emerge with relativity. Excitations can carry magnetic-flux units.
Adding electron-deficient materials, with three electrons in highest orbital, results in extra protons, because of electron vacancies {hole}|.
Two semiconductors can have insulator between them {Josephson junction}. Microwaves can supply energy to electron pairs. Voltage V is n = 1/2, 1, 3/3, or 2 times Planck's constant h times frequency f divided by electron charge e: V = (n*h*f) / (2*e). Third semiconductor can supply control current. Control current sets voltage at zero or one, using quantum-mechanical tunneling.
Two semiconductors, or semiconductor and conductor, can meet in region {junction}| 50 molecules thick. Contact point between metal and semiconductor has resistance that does not follow Ohm's law, because current depends on surface properties.
Semiconductors {metal oxide semiconductor} (MOS) can be metal oxides, which can be unipolar, rather than just bipolar.
Solid-state semiconductor circuit elements {transistor, electronic}| amplify current.
types
N-type semiconductor, P-type semiconductor, and N-type semiconductor can join in sandwich {NPN transistor}. P-type semiconductor, N-type semiconductor, and P-type semiconductor can join in sandwich {PNP transistor}. NPN or PNP transistors are bipolar transistors {junction transistor}, with two junctions. Weak signals control current flow. Junction transistors are current operated.
parts
Transistors have cathode emitter, anode collector, and base controller. Collector is between emitter and base. In PNP transistors, electrons flow from emitter to middle collector and from base to middle. In NPN transistors, electrons flow from middle collector to emitter and from middle to base.
process
Holes and electron diffusion across semiconductor np junction continues until electric force equilibrium, preventing further diffusing. Voltage is across emitter and base and across collector and emitter. Applying small positive charge to base attracts electrons and amplifies current 10^5 times. Electron flow from emitter to collector multiplies directly with voltage from base to emitter.
surface barrier
A depletion layer {space charge, transistor} between metal and semiconductor can control conductivity {point contact semiconductor} {surface barrier transistor}.
field effect
Electric field at right angles to silicon surface causes lateral conductance {field-effect transistor}. Insulated field plate can have field that induces conducting surface channel between two surface pn junctions {gate}, as in field-effect transistors, such as metal oxide semiconductors. Field-effect transistors have slow response and high impedance. They are voltage operated, rather than current operated.
electron tubes
Transistors can replace all electron tube types.
In PNP transistors, electrons flow from emitter to collector, and from other sandwich side {base, transistor} to middle.
In PNP transistors, electrons flow from emitter to middle {collector, transistor}, and from base to middle.
In PNP transistors, electrons flow from one sandwich side {emitter, transistor} to collector, and from base to middle.
At low temperatures, substances can be electrical conductors {superconductor} with no electrical resistance {superconductivity}|. Liquid oxygen, liquid nitrogen, and liquid hydrogen are superconductors. Organic crystals, metal oxides, and insulators can have superconductivity.
high temperature
Most high-temperature superconductors are copper oxide {cuprate} layers between other layers. Mercury-barium-calcium copper oxide superconducts at 164 K under 10,000 atm pressure and at 138 K at 1 atm.
Iron and arsenic layers between a lanthanum, cerium, samarium, neodymium, or praseodymium layer and an oxygen or fluoride layer can superconduct up to 52 K. Magnesium boride superconducts at 39 K. Bismuth, strontium, calcium, copper, and oxygen atoms can combine to make BSCCO high-temperature superconductor. Yttrium, barium, copper, and oxygen atoms can combine to make YBCO high-temperature superconductor.
cause
Large-scale quantum effects cause superconductivity, which happens when energies are small, such as at low temperature. Bosons in same quantum state can condense {Bose-Einstein condensation, superconductivity} (BEC) from gas to liquid. Repulsive bosons condense better. Materials can Bose-Einstein-condense at cold temperatures.
Fermions, such as electrons, form Cooper pairs at temperature lower than temperature at which material becomes degenerate Fermi gas. Both electrons have same spin. Making electron pairs makes positive metal ions. Cooper pairs have streamline flow through metal ions and travel with no resistance.
Fermions can pair more easily if attraction increases. Electrons can resonate {Feshbach resonance} in magnetic fields {magnetic resonance} and so pair better.
Magnetic flux has quanta in superconductors. Electric field has no quanta but quantizing it can make calculations easier.
magnetic field
Outside magnetic field can enter only short distance into superconductors with current, because photons acquire mass as electromagnetic gauge symmetry breaks spontaneously.
insulator
Forcing atoms {Mott insulator} in Bose-Einstein condensates to have definite positions changes quantum properties.
In superconducting materials, electrons distort positive-ion lattice to make phonons, which interact with other electrons, causing attraction and electron pairing {BCS theory}. Critical temperature is higher if more electrons can go to superconductive state, if lattice-vibration frequencies are higher, and if electrons and lattice interact stronger. Mercury-barium-calcium copper oxide does not follow BCS theory. Magnesium boride follows BCS theory. Liquid oxygen, liquid nitrogen, and liquid hydrogen follow BCS theory.
Fermions can pair {Cooper pair} at temperatures much lower than temperature at which system is degenerate Fermi gas.
Systems {degenerate Fermi gas} can have one fermion in each low-energy quantum state.
Devices {transition edge sensor} can detect photons at transition temperature to superconductivity.
Electric charges can flow past a point over time {current, electricity}| {electric current}. Flowing charge has one-tenth light speed.
Current I per area A {current density}| equals conductivity K times electric field E: I/A = K*E. Current I equals current density j times cross-sectional area A: I = (I/A) * A = j*A.
Current tends to stay on conducting-material surface {skin effect}, because electrons repel each other.
Charge flow can alternate directions over time {alternating current}| (AC). Alternating voltages cause electrons to oscillate. Commercial alternating current oscillates at 60 Hz in USA and 50 Hz in most other countries.
comparison
Direct current has less power loss and more average power than alternating current.
voltage
In alternating-current circuits, average or effective voltage equals maximum voltage divided by square root of two. In alternating-current circuits, average or effective current equals maximum current divided by square root of two.
transformer
Transformers change alternating-current voltage.
Charge flow can be in one direction only {direct current}| (DC). Direct current has less power loss and more average power than alternating current. Adding voltage sources alters direct-current voltage.
Charges must flow from source around loop back to source {circuit, electricity}| {electric circuit, flow}. At circuit points, current that goes in must equal current that comes out. Voltages around circuit loops must add to zero. Otherwise, electron density increases somewhere in circuit.
Earth {ground, electricity}|, or conductor leading to Earth, is an electron sink. Earth has many molecules and can absorb or give any number of charges without changing potential.
Circuit current and voltage follow laws {Kirchoff's laws} {Kirchoff laws}. Kirchoff's laws apply to circuit steady state. Transiently, Kirchoff's laws can break.
At circuit points, current coming in equals current going out. If current flowing in did not equal current flowing out, charge builds or falls at point and repels or attracts incoming charges, to make net charge return to zero.
Around circuit loops, voltages add to zero. If voltages around loop do not add to zero, extra voltage sends more charges to low-voltage point and so makes sum of voltages become zero again.
Wave-front amplitude or phase modifications {modulation, electricity}| can carry information on carrier waves. Information can vary amplitude {amplitude modulation, circuit} (AM) or frequency {frequency modulation, circuit} (FM). Frequency modulation carries temporal information along propagation line. Amplitude modulation carries spatial information perpendicular to propagation line.
Circuits {short circuit}| can have almost no resistance, allowing very high current.
RC, RL, and RLC circuits have reactance and resistance vector sum {impedance}|. Voltage equals impedance times current. Maximum power has equal source and circuit impedances.
Inductance and capacitance {reactance}| aid or impede current flow by storing and releasing energy, without heat loss.
comparison
Resistance opposes current and has heat loss.
phase
Reactance causes lag between voltage and current. In inductors, high frequency makes big current change and so large voltage. High inductance makes current changes make big voltage changes. Inductive reactance R equals two times pi times frequency f times inductance L: R = 2 * pi * f * L. In capacitors, high frequency makes voltage stay low, because little charge can build up. High capacitance requires large charge to make voltage, so voltage stays low. Capacitive reactance R equals reciprocal of two times pi times frequency f times capacitance C: R = 1 / (2 * pi * f * C).
Electrical devices {capacitor} {capacitance}| can store electrical energy. Electric-energy storage ability C is charge Q divided by voltage V: C = Q / V. Capacitance C equals material dielectric strength d times length l divided by cross-sectional area A: C = d * l / A.
field
In capacitors, electric field stores energy E: E = 0.5 * Q * V = 0.5 * C * V^2.
current
Electric-field energy builds as current flows. Electric-field energy tends to push current out. Current I is capacitance C times voltage change dV over time change dt: I = (1 / C) * dV / dt. Current and voltage are out of phase.
parallel plates
In parallel-plate capacitors, capacitance C equals electric permittivity e times dielectric constant k times cross-sectional area A divided by distance d between plates: C = e * k * A / d. Electric field between plates is constant and perpendicular to plates. If plates are farther apart, charge separation is more, voltage is more, and capacitance is less. If plate area is larger, charges spread out more, voltage is less, and capacitance is more. If dielectric constant is greater, material between plates has more polarization, field is less, voltage is less, and capacitance is more.
examples
Disk capacitors and rod capacitors work like parallel-plate capacitors. Two aluminum pie plates can make capacitor. Leyden jars can store charge as capacitance. Electrolytic capacitors allow only one-way current.
Circuits with current can store magnetic energy {inductance}|. Circuit devices {inductor} can store magnetic energy. Inductors are wire coils, so current makes strong magnetic field down coil middle. Soft iron bar can be in middle.
energy
Energy stored depends on current change compared to voltage. Inductance L is voltage V divided by current change dI with time change dt: L = V / (dI/dt). V = L * dI/dt. Magnetic-field energy builds as current flows. Magnetic-field energy tends to push current to stop. Current and voltage are out of phase. Magnetic-field energy E equals half inductance L times current I squared: E = 0.5 * L * I^2.
factors
Inductance increases as coil area increases, current-change frequency decreases, space magnetic-permeability increases, current decreases, voltage increases, coil-turn number decreases, and inductor length increases.
mutual inductance
Two coils with current have mutual inductance.
Circuit loads can be on separate wires {parallel circuit}|. Loads split currents. Voltages are equal. If circuit voltage sources are on separate wires, currents add, and voltages are equal. For resistances in parallel, resistance reciprocals add to equal total-resistance reciprocal, because cross-sectional area is more. Capacitances in parallel add, because area is more. For inductances in parallel, inductance reciprocals add to equal total-inductance reciprocal, because area is more.
Circuit loads can be in same wire {series circuit}|. Currents through loads are equal. Loads split voltages. If circuit voltage sources are in same wire, currents through loads are equal and voltages add. Resistances in series add, because length is longer. For capacitances in series, capacitance reciprocals add to equal total-capacitance reciprocal, because distance is more. Inductances in series add, because length is more.
Two circuits {coupled circuit} can share impedance, allowing energy transfer.
Circuits {filter circuit} can transmit frequency range, while blocking other frequencies. Filter circuits can remove frequency range, while allowing other frequencies, by differentiating or averaging. Circuits can choose different frequencies {selectivity, filter}. Frequency filtering sharpens edges, because edges have high frequency, and blurs have low frequency.
Circuits {LC circuit} can have inductor and capacitor. Energy flows from inductance magnetic field to capacitance electric field and then from capacitance electric field to inductance magnetic field, at resonance frequency. In resonating circuits, capacitance and inductance reactances are equal, so total reactance equals zero.
Circuits {RC circuit} can have resistor and capacitor. Voltage V depends on time t: V = Vo * e^(-t / (R*C)). Switching on circuit makes voltage build up in capacitor as field builds. Current lags behind voltage. At voltage alternation frequency, circuit resonates.
Circuits {RL circuit} can have inductance and resistor. Current I depends on time t: I = Io * e^(-t * R / L). At switching on, current changes fast, so voltage in coil is high. Then current becomes constant so voltage goes to zero, and current lags behind voltage. At current-alternation frequency, circuit resonates.
Thermionically emitted electrons can travel in beams, under side-electromagnet control, to fluorescent screens, where they excite phosphor crystals to make light {cathode ray tube}|. Cathode ray tubes are in TVs and oscilloscopes.
Circuit devices {detector} can select one signal from several.
Solid-state semiconductor circuit elements or vacuum tubes {diode}| can allow current to flow in only one direction. Diodes change alternating current to direct current. Tubes can have cathode emitter and anode plate. If plate is positive, emitted electrons flow toward plate. If plate is negative, no emitted electrons flow. For solid state, np junction allows charge to flow only in one direction, from P-type to N-type, with high resistance in other direction.
Circuit devices {mixer, signal} {electric circuit, mixer} can combine frequency signals.
Circuit devices {oscillator, circuit}| {electric oscillator} can change voltage waveform to other frequencies and amplitudes.
Devices {rectifier}| can change alternating to direct current.
Devices {rheostat}| can make variable resistance.
Circuit devices {wave shaper} can change voltage waveform.
Sunlight electric potential can make electric current in materials {photocell}|.
Shining light onto selenium {selenium cell} increases conductivity, because light increases electric field.
Instruments {ammeter}| can measure currents.
Instruments {galvanometer}| can measure small currents and current direction.
Instruments {ohmmeter}| can measure resistance.
Instruments {potentiometer}| can measure voltages at zero current, as ratio to exactly known voltage.
Instruments {voltmeter}| can measure electric potentials.
Devices {Wheatstone bridge}| can find resistance or capacitance in circuits using ratios. Wheatstone bridges eliminate voltage effects. AC current negates overall flow effects.
Current from a potential source P splits between two known resistances, R1 and R2, which have a galvanometer G across their endpoints to measure current and voltage (Figure 1). From one endpoint is an adjustable resistance Rv. From the other endpoint is an unknown resistance Rx. The resistances Rv and Rx meet at a point. If the ratio of the adjustable resistance Rv to the first known resistance R1 equals the ratio of the unknown resistance Rx to the second known resistance R2, the galvanometer has zero voltage and current.
For typical resistances, one can set R1 = R2, so Rv = Rx at galvanometer zero current and voltage.
If three resistances are known and one unknown, the measured voltage allows calculating the unknown resistance.
Wheatstone bridges can also find capacitance.
Relativistic electric-charge motion can caused electric force {magnetism, force}|. Magnetic fields have no net charge to stationary observers.
special relativity
Atoms and molecules have equal numbers of protons and electrons and so no net electric charge. Protons are in nuclei. Electrons orbit nuclei at 10% light speed. At that speed, motions have relativistic effects, and observers see length contraction. Stationary protons observe moving electrons, and electrons observe moving protons. Length contraction makes charges appear closer together along motion-direction line. Moving-charge density appears higher than stationary-charge density, making net electric force. Electric-charge number does not change, but relative distance decreases.
materials: iron
If electron orbits do not align, relativistic effects have all directions, and net force is zero. If electron orbits align, as in ferromagnetic materials, net force is not zero, and material has magnetism.
materials: conductors
Conductors have fixed protons and easily transferable electrons, with no net charge. Electric current moves electrons in wires at 10% light speed. Relativistic length contraction makes apparent increase in relative electric-charge density and apparent electric force. Current makes magnetism.
non-magnetic materials
People and non-magnetic materials have random molecule orientations and so no net magnetic effects.
no dipoles
Apparent electric charge in magnetism is not induced charge. Magnetism has no dipoles.
strength
At 10% light speed, relative electric-charge density increases by 1%, so magnetism is approximately one-hundredth electric-force strength. Larger currents make stronger magnetic forces. Electric generators and motors use many wires with high currents, to make strong magnetism.
direction
Electric longitudinal force between charges is along line between charge centers. Because it has no net charge, magnetic apparent-electric force cannot be along line between apparent charge centers. Magnetic transverse force is across line between apparent charges, along motion line, because apparent charge density increases only along motion line.
attraction and repulsion
Like electric force, magnetic force depends on interactions between charges. Like electric force, magnetic force can be attractive or repulsive. If apparent moving charges and stationary charges are both positive or both negative, magnetism is repulsive, because charges observe like charges. If apparent moving charges and stationary charges have opposite charge, magnetism is attractive, because charges observe unlike charges.
Wires at Rest with No Current
Charges are equal on both wires, and there is no movement and so no relativistic effects, so net force is zero. See Figure 1.
Wires at Rest and One Wire with Current
Stationary protons on wire with current see stationary protons and stationary electrons on other wire and so see no relativistic effects. Stationary protons on wire with no current see stationary protons and moving electrons on other wire and so see relativistic negative charge, making attractive force. Stationary electrons on wire with no current see stationary protons moving electrons on other wire and so see relativistic negative charge on other wire, making repulsive force. Moving electrons on wire with current see moving protons and moving electrons on other wire and so see relativistic effects, but they cancel. One force is attractive and one is negative, so net force is zero. See Figure 2.
Wires at Rest and Opposite Currents
Protons in both wires see stationary protons and moving electrons in other wire and so see relativistic negative charge on other wire, making attractive force. Electrons in both wires see moving protons and moving-twice-as-fast electrons and so see net relativistic negative charge on other wire, making large repulsive force. Net force is repulsion. See Figure 3.
Wires at Rest and Same Currents
Protons in both wires see stationary protons and moving electrons in other wire and so see relativistic negative charge on other wire, making attractive force. Electrons in both wires see stationary electrons and moving protons in other wire and so see relativistic positive charge on other wire, making attractive force. Net force is attraction. See Figure 4.
Stationary Conductor and Stationary Test Charge
See Figure 5. Stationary conductors, with equal numbers of fixed protons and easily movable electrons, have no net charge. Electric field from protons is equal and opposite to electric field from electrons, so there is no net electric field. Conductor is not moving relative to anything, so there are no relativistic effects. Stationary single negative test charge has electric field but feels no net force from conductor, because conductor has no net charge. Test charge is not moving relative to anything, so there are no relativistic effects. Net force is zero.
Stationary Conductor and Moving Test Charge
See Figure 6. Stationary conductors have no net electric field. Negative charge moves downward at constant velocity. Constantly moving charge has constant concentric magnetic field, which represents magnetic-force direction and strength that it exerts if it observes apparent charges. Test charge feels no net electric force from conductor, because conductor has no net charge. Test charge moves relative to both electrons and protons in conductor, so there is no net relativistic effect. Net force is zero.
Moving Conductor and Stationary Test Charge
See Figure 7. Conductor moves downward at constant velocity. Electric field from protons is equal and opposite to electric field from electrons, so there is no net electric field. Magnetic field from moving protons is equal and opposite to magnetic field from moving electrons, so there is no net magnetic field. Negative charge is stationary. Test charge feels no net electric force from conductor, because conductor has no net charge. Test charge moves relative to both electrons and protons in conductor, so there is no net relativistic effect. Net force is zero.
Moving Conductor and Moving Test Charge
See Figure 8. Conductor moves downward at constant velocity. Net electric and magnetic fields are zero. Negative charge moves downward at constant velocity. Test charge feels no net electric force from conductor, because conductor has no net charge. Test charge is not moving relative to either electrons or protons in conductor, so there are no relativistic effects. Net force is zero.
Moving Electrons in Stationary Conductor and Stationary Test Charge
See Figure 9. Conductor electrons move downward at constant velocity. Electric field from protons is equal and opposite to electric field from electrons, so there is no net electric field. Moving electrons make magnetic field. Negative charge is stationary. Test charge feels no net electric force from conductor, because conductor has no net charge. Test charge is not moving relative to protons in conductor, so there is no relativistic effect. Test charge moves relative to electrons in conductor and sees relativistic negative charge, making repulsive force.
Moving Electrons in Stationary Conductor and Moving Test Charge
See Figure 10. Conductor electrons move downward at constant velocity. Electric field from protons is equal and opposite to electric field from electrons, so there is no net electric field. Moving electrons make magnetic field. Negative charge moves downward at constant velocity. Test charge feels no net electric force from conductor, because conductor has no net charge. Test charge is not moving relative to electrons in conductor, so there is no relativistic effect. Test charge moves relative to protons in conductor and so sees relativistic positive charge, making attractive force.
Electric-charge relativistic motion causes weak electric force {magnetic force}| transverse to motion direction. Magnetic fields are electric fields caused by relativistic charge motions that make excess electrons or protons appear. Magnetic fields have no net charge to stationary observers.
examples
Wire in magnet field, tube and magnet, TV tube and magnet, two wires with current, and carpenter's bubble illustrate magnetic fields.
force
Magnetic force F equals moving charge q times velocity v times stationary-object magnetic field B times sine of angle A of approach to stationary object: F = q * v * B * sin(A). Magnetic force F equals wire current I times wire length L times stationary-object magnetic field B times sine of angle A between wire and stationary object: F = I * L * B * sin(A). Magnetic force F equals space magnetic permeability k' times wire current I1 times current I2 in other wire divided by distance r between wires: F = k' * I1 * I2 / r.
distance
Magnetic force depends on distance between wires, not distance squared, because relativistic effects are transverse to current motion.
Torques require moments {magnetic moment}. Magnetic moment M equals current i times coil area A: M = i * A. Magnetic moment equals pole strength p times path length l: M = p * l.
If positive current points in right-hand finger direction {right hand rule, magnetism}|, magnetic-field direction {north magnetic pole} points in thumb direction. The opposite direction is the other pole {south magnetic pole}.
Magnetic dipoles have magnetic force lines {magnetic field}| {flux density} {magnetic intensity} {magnetic induction}, from south pole to north pole. Magnetic field H is magnetic force F divided by pole strength p: H = F/p.
wire
Around wires, magnetic field H is space magnetic permeability k' times current I divided by two times pi times distance d from wire: H = (k' * I) / (2 * pi * d). Around solenoids, magnetic field H is space magnetic permeability k' times wire-turn number n times current I: H = k' * n * I. Around toroids, magnetic field H is space magnetic permeability k' times wire-turn number n times current I divided by two times pi times toroid radius r: H = (k' * n * I) / (2 * pi * r).
direction
Positive current in thumb direction makes magnetic field that circles conductor in right-hand finger direction {right hand rule, magnetic field}.
Numbers {magnetic flux}| of magnetic-field lines go through areas.
Magnetic field B times distance ds charge moves in field equals field magnetic permeability µ times current I {Ampere's circuital law} {Ampere circuital law} {Ampere's law}: integral of B * ds = µ * I. Current flows inside path of distance.
Because relativistic effects have small energies, atoms have quantized electric and magnetic fields. Magnetism quantum {Bohr magneton} is small magnetic pole.
Magnetic field relates to magnetic flux {Biot-Savart law}.
Energy conservation causes voltage from electromagnetic induction to make magnetic field opposed to original magnetic field {Lenz law}.
In dynamos or motors, electric and magnetic forces induce currents and voltages {electromagnetic induction}|.
outside force
If force moves conducting material through magnetic field or moves magnetic field near conducting material, protons and electrons in conductor move relative to protons and electrons that caused magnetic field. Moving protons and electrons make two electric currents that make two magnetic fields around conductor. Outside force provides energy to make magnetic fields.
However, no net charge moves, and test charges detect no electric current, because protons and electrons move together, so charges cancel.
induction
The original magnetic field interacts with both generated magnetic fields, setting up relativistic electric forces. Forces move electrons in conductor, but protons cannot move. Moving electrons make electric current opposite to movement and create magnetic field around current opposite in polarity to original magnetic field. Magnetic field created by moving electrons tends to resist relative movement between conductor and original magnetic field.
moving wire
For example, wire can moves through magnetic field. Moving wire moves wire protons and electrons, creating proton current and electron current, and currents make magnetic field around motion direction. Original magnetic field interacts with moving magnetic fields. Wire electrons are free and move down wire. Wire protons cannot move, though they feel magnetic force in opposite direction. Net current appears. Relativistic electric force separates electrons from protons, to make voltage that then makes current.
Energy for charge separation comes from outside mechanical energy used to move wire through magnetic field. Induced current makes net magnetic field that resists wire movement. Mechanical energy used to move wire makes electric field, induces current, and creates induced magnetic field.
energy transfers
In electromagnetic induction, potential energy in electric field causes voltage that makes current with kinetic energy, then current makes magnetic field with potential energy, then magnetic field slows current and builds voltage, which is potential energy in electric field. Cycle repeats.
Electric field and magnetic field, and voltage and current, are out of phase, because energy in one transfers to the other and then back again.
When electric-field change is zero and electric field maximizes, voltage maximizes and current is zero, and magnetic-field change maximizes and magnetic field is zero. As electric field decreases to zero, voltage decreases and current increases. As current increases, magnetic field increases and maximizes when current maximizes, electric-field change maximizes, and electric field is zero. As magnetic field decreases to zero, voltage increases and current decreases. As voltage increases, electric field increases and maximizes when voltage maximizes and electric field change is zero. Magnetic-field phase lags electric-field phase by 90 degrees.
examples
Electromagnetic induction happens in dollar bills in magnet, inductance coils, transformers, solenoids with iron bars, motors, and generators.
In conductors with current in magnetic fields, magnetic field pushes charges to conductor sides and makes electric field {Hall resistance, magnetism} opposed to magnetic field. Hall resistance varies with magnetic field and current.
semiconductor
In semiconductors, high magnetic field separates charges across width, not length, and so causes transverse current {Hall effect}.
quantum Hall effect
Quantum Hall resistance {quantum Hall effect} is inverse of small positive integer n times Planck's constant h divided by electron charge e squared: (1/n) * (h/e^2).
spin
In semiconductor ribbons with electric current, magnetic field from spin-orbit coupling causes excess electrons with one spin on one edge and excess electrons with opposite spin on other edge {spin Hall effect}.
In conductors with current in magnetic fields, magnetic field forces charge to conductor sides and makes electric field opposed to magnetic field {Hall resistance, current}, that varies with magnetic field and current.
Wire coil with current creates magnet with north and south poles {magnetic dipole}|.
field
Magnetic-field direction relates to current direction. By right hand rule, if positive current points in right-hand finger direction, magnetic-field direction points in thumb direction for north magnetic pole, and the opposite direction is south magnetic pole.
force
Like magnetic poles repel. Opposite magnetic poles attract. Force between magnetic poles equals space magnetic permeability k' times one magnetic-pole strength P times other magnetic-pole strength p, divided by distance r between poles: F = k' * P * p / r.
pole
Current i times path length L is pole strength p: p = i*L. Pole strength p equals charge q times velocity v: p = q*v.
infinitesimal
Infinitesimal wire loops can have unit current {elementary magnet}, to make idealized unit dipoles.
Materials have ease {permeability, magnetism}| {magnetic permeability} {mu, permeability} {µ, permeability} by which magnetic fields can go through. Permeability depends on ease with which magnetic dipoles form. Magnetic force constant k' directly depends on permeability.
types
Ferromagnetic materials have molecular magnetic fields that can align with outside magnetic field to enhance it. Non-magnetic materials and empty space have no magnetic fields and allow magnetic field. Diamagnetic materials have magnetic fields that oppose outside magnetic field. Paramagnetic materials have magnetic fields that slightly enhance outside magnetic field.
Crystals with impurities have greatly increased magnetization after crystal imperfections are overwhelmed by pressure {Barkhausen effect}.
Magnets cannot hold magnetism at high temperature {Curie temperature}, because random motions become great enough to cancel net magnetism.
In materials, all molecules in microscopic regions {domain, magnetism}| can have same magnetic-field alignment.
magnetization
After removing magnetization, domains return to original orientations {magnetic memory, domain}.
anistropy
Crystals magnetize differently on different axes {magnetocrystalline energy} {magnetocrystalline anisotropy}.
energy
Unaligned domains minimize magnetic-field potential energy {magnetostatic energy}. Boundaries between domains add potential energy {domain wall energy}. Domain-wall width increases by exchange energy but decreases by magnetocrystalline energy.
length
Crystals change length when magnetized, because domains shift {magnetostrictive energy}. Iron gets longer. Nickel gets shorter.
Electrical resistance can increase with increased magnetic field strength {extraordinary magnetoresistance} (EMR). Non-magnetic indium antimonide is a narrow gap semiconductor with high carrier mobility. Indium antimonide and gold lattice at room temperature has high EMR and so can be a magnetic-field sensor. Magnetic fields can change manganese oxide {manganite} from non-magnetic to ferromagnetic and metallic {colossal magnetoresistance} (CMR). Ferromagnetic layers with non-magnetic material between them {giant magnetoresistance} (GMR) are in disk-drive read heads.
External magnetic-field change changes material magnetization, after a time delay {hysteresis, magnetism}|. In motors and generators, external magnetic-field changes cycle, and material changes have time-delayed cycles {hysteresis loop}, with heat losses. Magnetic memory devices {twistor, memory} can use hysteresis loops.
Magnets can align all domains and have maximum magnetization {saturation, magnetism}|.
Magnetic materials {spin-glass} can have disordered magnetic domains that couple and make long-range effects.
Outside magnetic field causes weak, oppositely acting magnetism {diamagnetism}| in all materials. Outside magnetic field changes atom electron spins and electron orbits. Bismuth has the most diamagnetism. Two diamagnetic materials repel each other.
Solenoid coils can have large magnetic field that points down middle in one direction {electromagnet}|.
Outside magnetic field can induce weak enhancing magnetism {paramagnetism}| in materials, by affecting permanent magnetic dipole moment caused by unpaired-electron spin. Manganese, palladium, and metallic salts are paramagnetic. Paramagnetism is slightly stronger than diamagnetism. Higher temperature increases paramagnetism, by making longer dipoles. Two paramagnetic materials attract each other, because they have magnetic dipoles.
In materials, paramagnetism {ferrimagnetism}| can subtract from magnetic field. Manganese oxide is ferrimagnetic.
Materials can have asymmetric electron distributions in molecule outer orbits {ferromagnetism}|. Odd number of electrons allows materials to have permanent magnetism.
examples
Iron, nickel, cobalt, alnico alloy, liquid oxygen, lodestone, iron particles, magnetite, and ferrite have ferromagnetism.
alignment
Atom spins can align in same direction in microscopic domains. Electrostatic forces {exchange energy} align magnetic dipoles in domain. Magnets can align all domains in same orientation to make net magnetic field.
Hard ferromagnetic materials {permanent magnet}| holds magnetism even in another magnetic field. Soft-metal ferromagnets {soft magnet} lose or change magnetism in another magnetic field.
A metal disk {magnetic brake} rotating between two permanent magnets dissipates energy, because eddy currents make magnetic field opposed to permanent magnetic field and slow disk.
After removing magnetization, magnetic domains return to original orientations {magnetic memory, computer}.
Devices {solenoid}| can have wire coils. If current is in coils, magnetic field is sum of coil magnetic fields. Large magnetic field points down coil middle. Soft iron core in coil middle increases magnetic field by adding atom magnetic fields.
Devices {transformer}| can transfer voltage from circuit with alternating current to voltage from second circuit with alternating current. Transformers induce current in stationary-wire second coil using alternating current in first coil. Power in first coil equals power in second coil. Power is circuit voltage V times wire current I times wire-coil number n: V1 * I1 * n1 = V2 * I2 * n2.
Electronics can use electron charge and spin {spintronics} {magneto-electronics}. Flowing-electron spins {spin current} can align {spin-polarized}.
resistance
Electrical resistance {magnetoresistance} can change in different-polarization magnetic layers. Electrons take curved paths, slow in current direction, and decrease current. Computer hard drives can use magnetoresistant read heads [1998].
spin
Quantum spintronics can control single-electron spin. When nitrogen atoms replace carbon atoms in diamond, adjacent locations can be empty {nitrogen-vacancy center} (N-V center). Doped diamonds can semiconduct. N-V centers make single fluorescing electrons with two energy levels, with no ionization.
Mechanical energy can turn metal coil in magnetic field to generate electric current {generator, electricity} {electric generator}.
current
Electric current is in coil leading and trailing edges. Current changes direction with coil half turns, to make alternating current.
voltage
Voltage V equals magnetic field H times wire movement velocity v times wire-coil length l: V = H*v*l. Voltage V equals magnetic field H times area change dA divided by time change dt: V = H * dA / dt. Voltage V equals flux change dF divided by time change dt. V = dF / dt. Voltage V equals mutual inductance I times current change di divided by time change dt. V = I * di / dt.
example
Water from dams or steam from steam engines can turn wire coils around steel shafts {rotor, generator}, which are inside permanent magnets. Magnets and rotation cause electric current to flow in coils. Electric current changes direction as coil flips.
AC or DC
Rotor shaft {commutator, generator} can have separate conductors {brush, generator} on halves to allow current to leave rotor as direct current. Large-generator shafts {armature} collect alternating current directly.
Alternating current in coil has alternating magnetic field that can interact with outside magnetic field to make magnetic force on coil leading and trailing edges, and so turn coil {electric motor}|.
parts
Direct current or alternating current causes magnetic field in stationary wire coils {stator, motor} and in rotating wire coils {rotor, motor}. As rotor turns, current can go in forward or backward direction, changing magnetic field direction, because rotor shaft has separate conductors {brush, motor} on halves. Rotor magnetic field continually pulls into alignment with stator field, turning rotor by magnetic force. Rotation angular momentum starts cycle again.
torque
Magnetic force causes torque on coil and makes both magnetic fields tend to align. Coil torque T equals coil number n times magnetic field B times current i times coil area A: T = n * B * i * A. When magnetic fields align, force or torque is zero. Just before magnetic fields align, current reverses in coil. Current can reverse every half circle using commutators. Current can reverse using alternating current at needed frequency.
torque: direction
Right-hand palm points in magnetic-force direction, fingers point in magnetic-field direction, and thumb points in positive-current direction {right hand rule, torque}.
types
Series motors have low back emf, high field, and high current when starting and low current, high back emf, and low field when running. Shunt motors have constant field and lower current at high speed. Series and shunt motors can combine. Electric motors use direct current {induction motor}, alternating current {synchronous motor}, or either {universal motor}.
Current can reverse every half circle using devices {commutator, motor}|.
Voltage is between two different touching metals at different temperatures, because metals have different electronegativities {thermoelectric effect}|. If metal rod has different temperatures at ends, voltage is between ends.
If two different metals have different temperatures and contact at two different places, circuit forms {Seebeck effect}.
Thermoelectric-effect voltage can measure temperature {thermocouple}|.
Thermocouples can be in series {thermopile}|.
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Date Modified: 2022.0225