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}|.
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Date Modified: 2022.0225