In physics the Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with a velocity v in an electric field E and a magnetic field B experiences a force of F = q E + q v × B. Variations on this basic formula describe the magnetic force on a current-carrying wire, the electromotive force in a wire loop moving through a magnetic field, the force on a charged particle which might be traveling near the speed of light. Historians suggest that the law is implicit in a paper by James Clerk Maxwell, published in 1865. Hendrik Lorentz arrived in a complete derivation in 1895, identifying the contribution of the electric force a few years after Oliver Heaviside identified the contribution of the magnetic force; the force F acting on a particle of electric charge q with instantaneous velocity v, due to an external electric field E and magnetic field B, is given by: where × is the vector cross product. In terms of cartesian components, we have: F x = q, F y = q, F z = q.
In general, the electric and magnetic fields are functions of the time. Therefore, the Lorentz force can be written as: F = q in which r is the position vector of the charged particle, t is time, the overdot is a time derivative. A positively charged particle will be accelerated in the same linear orientation as the E field, but will curve perpendicularly to both the instantaneous velocity vector v and the B field according to the right-hand rule; the term qE is called the electric force. According to some definitions, the term "Lorentz force" refers to the formula for the magnetic force, with the total electromagnetic force given some other name; this article will not follow this nomenclature: In what follows, the term "Lorentz force" will refer to the expression for the total force. The magnetic force component of the Lorentz force manifests itself as the force that acts on a current-carrying wire in a magnetic field. In that context, it is called the Laplace force; the Lorentz force is a force exerted by the electromagnetic field on the charged particle, that is, it is the rate at which linear momentum is transferred from the electromagnetic field to the particle.
Associated with it is the power, the rate at which energy is transferred from the electromagnetic field to the particle. That power is v ⋅ F = q v ⋅ E. Notice that the magnetic field does not contribute to the power because the magnetic force is always perpendicular to the velocity of the particle. For a continuous charge distribution in motion, the Lorentz force equation becomes: d F = d q where dF is the force on a small piece of the charge distribution with charge dq. If both sides of this equation are divided by the volume of this small piece of the charge distribution dV, the result is: f = ρ where f is the force density and ρ is the charge density. Next, the current density corresponding to the motion of the charge continuum is J = ρ v so the continuous analogue to the equation is The total force is the volume integral over the charge distr
A magnetic field is a vector field that describes the magnetic influence of electric charges in relative motion and magnetized materials. Magnetic fields are observed from subatomic particles to galaxies. In everyday life, the effects of magnetic fields are seen in permanent magnets, which pull on magnetic materials and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field vary with location; as such, it is an example of a vector field. The term'magnetic field' is used for two distinct but related fields denoted by the symbols B and H. In the International System of Units, H, magnetic field strength, is measured in the SI base units of ampere per meter. B, magnetic flux density, is measured in tesla, equivalent to newton per meter per ampere.
H and B differ in. In a vacuum, B and H are the same aside from units. Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. Magnetic fields and electric fields are interrelated, are both components of the electromagnetic force, one of the four fundamental forces of nature. Magnetic fields are used throughout modern technology in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric generators; the interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect; the Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass. Although magnets and magnetism were studied much earlier, the research of magnetic fields began in 1269 when French scholar Petrus Peregrinus de Maricourt mapped out the magnetic field on the surface of a spherical magnet using iron needles.
Noting that the resulting field lines crossed at two points he named those points'poles' in analogy to Earth's poles. He clearly articulated the principle that magnets always have both a north and south pole, no matter how finely one slices them. Three centuries William Gilbert of Colchester replicated Petrus Peregrinus' work and was the first to state explicitly that Earth is a magnet. Published in 1600, Gilbert's work, De Magnete, helped to establish magnetism as a science. In 1750, John Michell stated that magnetic poles attract and repel in accordance with an inverse square law. Charles-Augustin de Coulomb experimentally verified this in 1785 and stated explicitly that the north and south poles cannot be separated. Building on this force between poles, Siméon Denis Poisson created the first successful model of the magnetic field, which he presented in 1824. In this model, a magnetic H-field is produced by'magnetic poles' and magnetism is due to small pairs of north/south magnetic poles. Three discoveries in 1820 challenged this foundation of magnetism, though.
Hans Christian Ørsted demonstrated that a current-carrying wire is surrounded by a circular magnetic field. André-Marie Ampère showed that parallel wires with currents attract one another if the currents are in the same direction and repel if they are in opposite directions. Jean-Baptiste Biot and Félix Savart announced empirical results about the forces that a current-carrying long, straight wire exerted on a small magnet, determining that the forces were inversely proportional to the perpendicular distance from the wire to the magnet. Laplace deduced, but did not publish, a law of force based on the differential action of a differential section of the wire, which became known as the Biot–Savart law. Extending these experiments, Ampère published his own successful model of magnetism in 1825. In it, he showed the equivalence of electrical currents to magnets and proposed that magnetism is due to perpetually flowing loops of current instead of the dipoles of magnetic charge in Poisson's model.
This has the additional benefit of explaining. Further, Ampère derived both Ampère's force law describing the force between two currents and Ampère's law, like the Biot–Savart law described the magnetic field generated by a steady current. In this work, Ampère introduced the term electrodynamics to describe the relationship between electricity and magnetism. In 1831, Michael Faraday discovered electromagnetic induction when he found that a changing magnetic field generates an encircling electric field, he described this phenomenon in. Franz Ernst Neumann proved that, for a moving conductor in a magnetic field, induction is a consequence of Ampère's force law. In the process, he introduced the magnetic vector potential, shown to be equivalent to the underlying mechanism proposed by Faraday. In 1850, Lord Kelvin known as William Thomson, distinguished between two magnetic fields now denoted H and B; the former applied to the latter to Ampère's model and induction. Further, he derived how H and B relate to each other
Alternating current is an electric current which periodically reverses direction, in contrast to direct current which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, it is the form of electrical energy that consumers use when they plug kitchen appliances, televisions and electric lamps into a wall socket. A common source of DC power is a battery cell in a flashlight; the abbreviations AC and DC are used to mean alternating and direct, as when they modify current or voltage. The usual waveform of alternating current in most electric power circuits is a sine wave, whose positive half-period corresponds with positive direction of the current and vice versa. In certain applications, different waveforms are used, such as square waves. Audio and radio signals carried on electrical wires are examples of alternating current; these types of alternating current carry information such as sound or images sometimes carried by modulation of an AC carrier signal.
These currents alternate at higher frequencies than those used in power transmission. Electrical energy is distributed as alternating current because AC voltage may be increased or decreased with a transformer; this allows the power to be transmitted through power lines efficiently at high voltage, which reduces the energy lost as heat due to resistance of the wire, transformed to a lower, voltage for use. Use of a higher voltage leads to more efficient transmission of power; the power losses in the wire are a product of the square of the current and the resistance of the wire, described by the formula: P w = I 2 R. This means that when transmitting a fixed power on a given wire, if the current is halved, the power loss due to the wire's resistance will be reduced to one quarter; the power transmitted is equal to the product of the voltage. Power is transmitted at hundreds of kilovolts, transformed to 100 V – 240 V for domestic use. High voltages have disadvantages, such as the increased insulation required, increased difficulty in their safe handling.
In a power plant, energy is generated at a convenient voltage for the design of a generator, stepped up to a high voltage for transmission. Near the loads, the transmission voltage is stepped down to the voltages used by equipment. Consumer voltages vary somewhat depending on the country and size of load, but motors and lighting are built to use up to a few hundred volts between phases; the voltage delivered to equipment such as lighting and motor loads is standardized, with an allowable range of voltage over which equipment is expected to operate. Standard power utilization voltages and percentage tolerance vary in the different mains power systems found in the world. High-voltage direct-current electric power transmission systems have become more viable as technology has provided efficient means of changing the voltage of DC power. Transmission with high voltage direct current was not feasible in the early days of electric power transmission, as there was no economically viable way to step down the voltage of DC for end user applications such as lighting incandescent bulbs.
Three-phase electrical generation is common. The simplest way is to use three separate coils in the generator stator, physically offset by an angle of 120° to each other. Three current waveforms are produced that are equal in magnitude and 120° out of phase to each other. If coils are added opposite to these, they generate the same phases with reverse polarity and so can be wired together. In practice, higher "pole orders" are used. For example, a 12-pole machine would have 36 coils; the advantage is. For example, a 2-pole machine running at 3600 rpm and a 12-pole machine running at 600 rpm produce the same frequency. If the load on a three-phase system is balanced among the phases, no current flows through the neutral point. In the worst-case unbalanced load, the neutral current will not exceed the highest of the phase currents. Non-linear loads may require an oversized neutral bus and neutral conductor in the upstream distribution panel to handle harmonics. Harmonics can cause neutral conductor current levels to exceed that of all phase conductors.
For three-phase at utilization voltages a four-wire system is used. When stepping down three-phase, a transformer with a Delta primary and a Star secondary is used so there is no need for a neutral on the supply side. For smaller customers only a single phase and neutral, or two phases and neutral, are taken to the property. For larger installations all three phases and neutral are taken to the main distribution panel. From the three-phase main panel, both single and three-phase circuits may lead off. Three-wire single-phase systems, with a single center-tapped transformer giving two live conductors, is a common distribution scheme for res
The magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include: loops of electric current, permanent magnets, elementary particles, various molecules, many astronomical objects. More the term magnetic moment refers to a system's magnetic dipole moment, the component of the magnetic moment that can be represented by an equivalent magnetic dipole: a magnetic north and south pole separated by a small distance; the magnetic dipole component is sufficient for large enough distances. Higher order terms may be needed in addition to the dipole moment for extended objects; the magnetic dipole moment of an object is defined in terms of the torque that object experiences in a given magnetic field. The same applied magnetic field creates larger torques on objects with larger magnetic moments; the strength of this torque depends not only on the magnitude of the magnetic moment but on its orientation relative to the direction of the magnetic field.
The magnetic moment may be considered, therefore. The direction of the magnetic moment points from the south to north pole of the magnet; the magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, decreases as the inverse cube of the distance from the object; the magnetic moment can be defined as a vector relating the aligning torque on the object from an externally applied magnetic field to the field vector itself. The relationship is given by: τ = m × B where τ is the torque acting on the dipole, B is the external magnetic field, m is the magnetic moment; this definition is based on how one could, in principle, measure the magnetic moment of an unknown sample. For a current loop, this definition leads to the magnitude of the magnetic dipole moment equaling the product of the current times the area of the loop. Further, this definition allows the calculation of the expected magnetic moment for any known macroscopic current distribution.
An alternative definition is useful for thermodynamics calculations of the magnetic moment. In this definition, the magnetic dipole moment of a system is the negative gradient of its intrinsic energy, with respect to external magnetic field: m = − x ^ ∂ U i n t ∂ B x − y ^ ∂ U i n t ∂ B y − z ^ ∂ U i n t ∂ B z. Generically, the intrinsic energy includes the self-field energy of the system plus the energy of the internal workings of the system. For example, for a hydrogen atom in a 2p state in an external field, the self-field energy is negligible, so the internal energy is the eigenenergy of the 2p state, which includes Coulomb potential energy and the kinetic energy of the electron; the interaction-field energy between the internal dipoles and external fields is not part of this internal energy. The unit for magnetic moment in International System of Units base units is A⋅m2, where A is ampere and m is meter; this unit has equivalents in other SI derived units including: A ⋅ m 2 = N ⋅ m T = J T, where N is newton, T is tesla, J is joule.
Although torque and energy are dimensionally equivalent, torques are never expressed in units of energy. In the CGS system, there are several different sets of electromagnetism units, of which the main ones are ESU, EMU. Among these, there are two alternative units of magnetic dipole moment: 1 statA ⋅ cm 2 = 3.33564095 × 10 − 14 A ⋅ m 2 1 erg G = 10 − 3 A ⋅ m 2,where statA is statamperes, cm is centimeters, erg is ergs, G is gauss. The ratio of these two non-equivalent CGS units is equal to the speed of light in free space, expressed in cm⋅s−1. All formula
An electrical insulator is a material whose internal electric charges do not flow freely. This contrasts with other materials and conductors, which conduct electric current more easily; the property that distinguishes an insulator is its resistivity. A perfect insulator does not exist, because insulators contain small numbers of mobile charges which can carry current. In addition, all insulators become electrically conductive when a sufficiently large voltage is applied that the electric field tears electrons away from the atoms; this is known as the breakdown voltage of an insulator. Some materials such as glass and Teflon, which have high resistivity, are good electrical insulators. A much larger class of materials though they may have lower bulk resistivity, are still good enough to prevent significant current from flowing at used voltages, thus are employed as insulation for electrical wiring and cables. Examples include rubber-like polymers and most plastics which can be thermoset or thermoplastic in nature.
Insulators are used in electrical equipment to support and separate electrical conductors without allowing current through themselves. An insulating material used in bulk to wrap electrical cables or other equipment is called insulation; the term insulator is used more to refer to insulating supports used to attach electric power distribution or transmission lines to utility poles and transmission towers. They support the weight of the suspended wires without allowing the current to flow through the tower to ground. Electrical insulation is the absence of electrical conduction. Electronic band theory says that a charge flows if states are available into which electrons can be excited; this allows electrons to gain energy and thereby move through a conductor such as a metal. If no such states are available, the material is an insulator. Most insulators have a large band gap; this occurs because the "valence" band containing the highest energy electrons is full, a large energy gap separates this band from the next band above it.
There is always some voltage. Once this voltage is exceeded the material ceases being an insulator, charge begins to pass through it. However, it is accompanied by physical or chemical changes that permanently degrade the material's insulating properties. Materials that lack electron conduction are insulators. For example, if a liquid or gas contains ions the ions can be made to flow as an electric current, the material is a conductor. Electrolytes and plasmas contain ions and act as conductors whether or not electron flow is involved; when subjected to a high enough voltage, insulators suffer from the phenomenon of electrical breakdown. When the electric field applied across an insulating substance exceeds in any location the threshold breakdown field for that substance, the insulator becomes a conductor, causing a large increase in current, an electric arc through the substance. Electrical breakdown occurs when the electric field in the material is strong enough to accelerate free charge carriers to a high enough velocity to knock electrons from atoms when they strike them, ionizing the atoms.
These freed electrons and ions are in turn accelerated and strike other atoms, creating more charge carriers, in a chain reaction. The insulator becomes filled with mobile charge carriers, its resistance drops to a low level. In a solid, the breakdown voltage is proportional to the band gap energy; when corona discharge occurs, the air in a region around a high-voltage conductor can break down and ionise without a catastrophic increase in current. However, if the region of air breakdown extends to another conductor at a different voltage it creates a conductive path between them, a large current flows through the air, creating an electric arc. A vacuum can suffer a sort of breakdown, but in this case the breakdown or vacuum arc involves charges ejected from the surface of metal electrodes rather than produced by the vacuum itself. In addition, all insulators become conductors at high temperatures as the thermal energy of the valence electrons is sufficient to put them in the conduction band.
In certain capacitors, shorts between electrodes formed due to dielectric breakdown can disappear when the applied electric field is reduced. A flexible coating of an insulator is applied to electric wire and cable, this is called insulated wire. Wires sometimes don't use an insulating coating, since a solid coating may be impractical. However, wires that touch each other produce cross connections, short circuits, fire hazards. In coaxial cable the center conductor must be supported in the middle of the hollow shield to prevent EM wave reflections. Wires that expose voltages higher than 60 V can cause human shock and electrocution hazards. Insulating coatings help to prevent all of these problems; some wires have a mechanical covering with no voltage rating—e.g.: service-drop, doorbell, thermostat wire. An insulated wire or cable has a maximum conductor temperature rating, it may not have an ampacity rating. In electronic systems, printed circuit boards are made from epoxy plastic and fibreglass.
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship: I = V R, where I is the current through the conductor in units of amperes, V is the voltage measured across the conductor in units of volts, R is the resistance of the conductor in units of ohms. More Ohm's law states that the R in this relation is constant, independent of the current. Ohm's law is an empirical relation which describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of current; however some materials do not obey Ohm's law, these are called non-ohmic. The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire.
Ohm explained his experimental results by a more complex equation than the modern form above. In physics, the term Ohm's law is used to refer to various generalizations of the law; this reformulation of Ohm's law is due to Gustav Kirchhoff. In January 1781, before Georg Ohm's work, Henry Cavendish experimented with Leyden jars and glass tubes of varying diameter and length filled with salt solution, he measured the current by noting how strong a shock he felt as he completed the circuit with his body. Cavendish wrote that the "velocity" varied directly as the "degree of electrification", he did not communicate his results to other scientists at the time, his results were unknown until Maxwell published them in 1879. Francis Ronalds delineated “intensity” and “quantity” for the dry pile – a high voltage source – in 1814 using a gold-leaf electrometer, he found for a dry pile that the relationship between the two parameters was not proportional under certain meteorological conditions. Ohm did his work on resistance in the years 1825 and 1826, published his results in 1827 as the book Die galvanische Kette, mathematisch bearbeitet.
He drew considerable inspiration from Fourier's work on heat conduction in the theoretical explanation of his work. For experiments, he used voltaic piles, but used a thermocouple as this provided a more stable voltage source in terms of internal resistance and constant voltage, he used a galvanometer to measure current, knew that the voltage between the thermocouple terminals was proportional to the junction temperature. He added test wires of varying length and material to complete the circuit, he found that his data could be modeled through the equation x = a b + l, where x was the reading from the galvanometer, l was the length of the test conductor, a depended on the thermocouple junction temperature, b was a constant of the entire setup. From this, Ohm published his results. In modern notation we would write, I = E r + R, where E is the open-circuit emf of the thermocouple, r is the internal resistance of the thermocouple and R is the resistance of the test wire. In terms of the length of the wire this becomes, I = E r + R l, where R is the resistance of the test wire per unit length.
Thus, Ohm's coefficients are, a = E R, b = r R. Ohm's law was the most important of the early quantitative descriptions of the physics of electricity. We consider it obvious today; when Ohm first published his work, this was not the case. They called his work a "web of naked fancies" and the German Minister of Education proclaimed that "a professor who preached such heresies was unworthy to teach science." The prevailing scientific philosophy in Germany at the time asserted that experiments need not be performed to develop an understanding of nature because nature is so well ordered, that scientific truths may be deduced through reasoning alone. Ohm's brother Martin, a mathematician, was battling the German educational system; these factors hindered the acceptance of Ohm's work, his work did not become accepted until the 1840s. However, Ohm received recognition for his contributions to science. In the 1850s, Ohm's law was known as such and was considered proved, alternatives, such as "Barlow's law", were discredited, in terms of real ap
Electrostatic discharge is the sudden flow of electricity between two electrically charged objects caused by contact, an electrical short, or dielectric breakdown. A buildup of static electricity can be caused by electrostatic induction; the ESD occurs when differently-charged objects are brought close together or when the dielectric between them breaks down creating a visible spark. ESD can create spectacular electric sparks, but less dramatic forms which may be neither seen nor heard, yet still be large enough to cause damage to sensitive electronic devices. Electric sparks require a field strength above 40 kV/cm in air, as notably occurs in lightning strikes. Other forms of ESD include corona discharge from sharp electrodes and brush discharge from blunt electrodes. ESD can cause harmful effects of importance in industry, including explosions in gas, fuel vapor and coal dust, as well as failure of solid state electronics components such as integrated circuits; these can suffer permanent damage.
Electronics manufacturers therefore establish electrostatic protective areas free of static, using measures to prevent charging, such as avoiding charging materials and measures to remove static such as grounding human workers, providing antistatic devices, controlling humidity. ESD simulators may be used to test electronic devices, for example with a human body model or a charged device model. One of the causes of ESD events is static electricity. Static electricity is generated through tribocharging, the separation of electric charges that occurs when two materials are brought into contact and separated. Examples of tribocharging include walking on a rug, rubbing a plastic comb against dry hair, rubbing a balloon against a sweater, ascending from a fabric car seat, or removing some types of plastic packaging. In all these cases, the breaking of contact between two materials results in tribocharging, thus creating a difference of electrical potential that can lead to an ESD event. Another cause of ESD damage is through electrostatic induction.
This occurs when an electrically charged object is placed near a conductive object isolated from the ground. The presence of the charged object creates an electrostatic field that causes electrical charges on the surface of the other object to redistribute. Though the net electrostatic charge of the object has not changed, it now has regions of excess positive and negative charges. An ESD event may occur. For example, charged regions on the surfaces of styrofoam cups or bags can induce potential on nearby ESD sensitive components via electrostatic induction and an ESD event may occur if the component is touched with a metallic tool. ESD can be caused by energetic charged particles impinging on an object; this causes deep charging. This is a known hazard for most spacecraft; the most spectacular form of ESD is the spark, which occurs when a heavy electric field creates an ionized conductive channel in air. This can cause minor discomfort to people, severe damage to electronic equipment, fires and explosions if the air contains combustible gases or particles.
However, many ESD events occur without a audible spark. A person carrying a small electric charge may not feel a discharge, sufficient to damage sensitive electronic components; some devices may be damaged by discharges as small as 30 V. These invisible forms of ESD can cause outright device failures, or less obvious forms of degradation that may affect the long term reliability and performance of electronic devices; the degradation in some devices may not become evident until well into their service life. A spark is triggered when the electric field strength exceeds 4–30 kV/cm — the dielectric field strength of air; this may cause a rapid increase in the number of free electrons and ions in the air, temporarily causing the air to abruptly become an electrical conductor in a process called dielectric breakdown. The best known example of a natural spark is lightning. In this case the electric potential between a cloud and ground, or between two clouds, is hundreds of millions of volts; the resulting current.
On a much smaller scale, sparks can form in air during electrostatic discharges from charged objects that are charged to as little as 380 V. Earth's atmosphere consists of 78 % nitrogen. During an electrostatic discharge, such as a lightning flash, the affected atmospheric molecules become electrically overstressed; the diatomic oxygen molecules are split, recombine to form ozone, unstable, or reacts with metals and organic matter. If the electrical stress is high enough, nitrogen oxides can form. Both products are toxic to animals, nitrogen oxides are essential for nitrogen fixation. Ozone is used in water purification. Sparks are an ignition source in combustible environments that may lead to catastrophic explosions in concentrated fuel environments. Most explosions can be traced back to a tiny electrostatic discharge, whether it was an unexpected combustible fuel leak invading a known open air sparking device, or an unexpected spark in a known fuel rich environment; the end result is the same if oxygen is present and the three criteria of the fire triangle have been combined.
Many electronic components microchips, can be damaged by ESD. Sensitive components need to be protected during and after manufacture, during shipping and device assembly