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 Electricity generation

From Wikipedia, the free encyclopedia

Electricity generation is the process of creating electricity from other forms of energy.

The fundamental principles of electricity generation were discovered during the 1820s and early 1830s by the British scientist Michael Faraday. His basic method is still used today: electricity is generated by the movement of a loop of wire, or disc of copper between the poles of a magnet.[1]

For electric utilities, it is the first process in the delivery of electricity to consumers. The other processes, electric power transmission, electricity distribution, and electrical power storage and recovery using pumped storage methods are normally carried out by the electrical power industry.

Electricity is most often generated at a power station by electromechanical generators, primarily driven by heat engines fueled by chemical combustion or nuclear fission but also by other means such as the kinetic energy of flowing water and wind. There are many other technologies that can be and are used to generate electricity such as solar photovoltaics and geothermal power.


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Multiple lightning strikes on a city at night

Electricity (from the New Latin ēlectricus, "amber-like"[a]) is a general term that encompasses a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena, such as lightning and static electricity, but in addition, less familiar concepts, such as the electromagnetic field and electromagnetic induction.

In general usage, the word "electricity" is adequate to refer to a number of physical effects. In scientific usage, however, the term is vague, and these related, but distinct, concepts are better identified by more precise terms:

Electrical phenomena have been studied since antiquity, though advances in the science were not made until the seventeenth and eighteenth centuries. Practical applications for electricity however remained few, and it would not be until the late nineteenth century that engineers were able to put it to industrial and residential use. The rapid expansion in electrical technology at this time transformed industry and society. Electricity's extraordinary versatility as a source of energy means it can be put to an almost limitless set of applications which include transport, heating, lighting, communications, and computation. The backbone of modern industrial society is, and for the foreseeable future can be expected to remain, the use of electrical power.[1]

Electric charge

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Electricity · Magnetism
Electric charge · Coulomb's law · Electric field · Electric flux · Gauss's law · Electric potential · Electrostatic induction · Electric dipole moment · Polarization density
Electric charge
Measured in (SI unit): coulomb
Commonly used symbols: Q
Expressed in other quantities: Q = I · t

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields. The interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces.

The electric charge on a body may be positive or negative. Two positively charged bodies experience a mutual repulsive force, as do two negatively charged bodies. A positively charged body and a negatively charged body experience an attractive force. The study of how charged bodies interact is classical electrodynamics, which is accurate insofar as quantum effects can be ignored.

Twentieth-century experiments demonstrated that electric charge is quantized: the charge of any system, body, or particle (except quarks) is an integer multiple of the elementary charge, e, approximately equal to 1.602×10−19 coulombs. The proton has a charge of e, and the electron has a charge of −e. The study of charged particles, and how their interactions are mediated by photons, is quantum electrodynamics.




Electric charge is a characteristic property of many subatomic particles. The charges of free-standing particles are integer multiples of the elementary charge e; we say that electric charge is quantized. Michael Faraday, in his electrolysis experiments, was the first to note the discrete nature of electric charge. Robert Millikan's oil-drop experiment demonstrated this fact directly, and measured the elementary charge.

By convention, the charge of an electron is −1, while that of a proton is +1. Charged particles whose charges have the same sign repel one another, and particles whose charges have different signs attract. Coulomb's law quantifies the electrostatic force between two particles by asserting that the force is proportional to the product of their charges, and inversely proportional to the square of the distance between them.

The charge of an antiparticle equals that of the corresponding particle, but with opposite sign. Quarks have fractional charges of either −13 or +23, but free-standing quarks have never been observed (the theoretical reason for this fact is asymptotic freedom).

The electric charge of a macroscopic object is the sum of the electric charges of the particles that make it up. This charge is often zero, because matter is made of atoms, and atoms all have equal numbers of protons and electrons. More generally, in every molecule, the number of anions (negatively charged atoms) equals the number of cations (positively charged atoms). When the net electric charge is non-zero and motionless, the phenomenon is known as static electricity. Even when the net charge is zero, it can be distributed non-uniformly (e.g., due to an external electric field or to molecular motion), in which case the material is said to be polarized. The charge due to polarization is known as bound charge, while the excess charge brought from outside is called free charge. The motion of charged particles (especially the motion of electrons in metals) in a given direction is known as electric current.


The SI unit of quantity of electric charge is the coulomb, which is equivalent to about 6.25 × 1018 e (e is the charge on a single electron or proton). Hence, the charge of an electron is approximately −1.602×10−19 C. The coulomb is defined as the quantity of charge that has passed through the cross-section of an electrical conductor carrying one ampere within one second. The symbol Q is often used to denote a quantity of electricity or charge. The quantity of electric charge can be directly measured with an electrometer, or indirectly measured with a ballistic galvanometer.

After finding the quantized character of charge, in 1891 Stoney proposed the unit 'electron' for this fundamental unit of electrical charge. This was before the discovery of the particle by J.J. Thomson in 1897. Today, the name "electron" for the unit of charge is no longer widely used except in the derived unit "electronvolt". This is quite surprising considering the wide use of this unit in the fields of physics and chemistry. The unit is today treated as nameless, referred to as "fundamental unit of charge" or simply as "e".

Formally, a measure of charge should be a multiple of the elementary charge e (charge is quantized), but since it is an average, macroscopic quantity, many orders of magnitude larger than a single elementary charge, it can effectively take on any real value. Furthermore, in some contexts it is meaningful to speak of fractions of a charge; e.g. in the charging of a capacitor.


As reported by the Ancient Greek philosopher Thales of Miletus around 600 BC, charge (or electricity) could be accumulated by rubbing fur on various substances, such as amber. The Greeks noted that the charged amber buttons could attract light objects such as hair. They also noted that if they rubbed the amber for long enough, they could even get a spark to jump. This property derives from the triboelectric effect.

In 1600 the English scientist William Gilbert returned to the subject in De Magnete, and coined the New Latin word electricus from ηλεκτρον (elektron), the Greek word for "amber", which soon gave rise to the English words "electric" and "electricity." He was followed in 1660 by Otto von Guericke, who invented what was probably the first electrostatic generator. Other European pioneers were Robert Boyle, who in 1675 stated that electric attraction and repulsion can act across a vacuum; Stephen Gray, who in 1729 classified materials as conductors and insulators; and C. F. du Fay, who proposed in 1733[1] that electricity came in two varieties which cancelled each other, and expressed this in terms of a two-fluid theory. When glass was rubbed with silk, du Fay said that the glass was charged with vitreous electricity, and when amber was rubbed with fur, the amber was said to be charged with resinous electricity. In 1839, Michael Faraday showed that the apparent division between static electricity, current electricity and bioelectricity was incorrect, and all were a consequence of the behavior of a single kind of electricity appearing in opposite polarities. It is arbitrary which polarity you call positive and which you call negative. Positive charge can be defined as the charge left on a glass rod after being rubbed with silk.[2]

One of the foremost experts on electricity in the 18th century was Benjamin Franklin, who argued in favour of a one-fluid theory of electricity. Franklin imagined electricity as being a type of invisible fluid present in all matter; for example he believed that it was the glass in a Leyden jar that held the accumulated charge. He posited that rubbing insulating surfaces together caused this fluid to change location, and that a flow of this fluid constitutes an electric current. He also posited that when matter contained too little of the fluid it was "negatively" charged, and when it had an excess it was "positively" charged. Arbitrarily (or for a reason that was not recorded) he identified the term "positive" with vitreous electricity and "negative" with resinous electricity. William Watson arrived at the same explanation at about the same time.

Static electricity and electric current

Static electricity and electric current are two separate phenomena, both involving electric charge, and may occur simultaneously in the same object. Static electricity is a reference to the electric charge of an object and the related electrostatic discharge when two objects are brought together that are not at equilibrium. An electrostatic discharge creates a change in the charge of each of the two objects. In contrast, electric current is the flow of electric charge through an object, which produces no net loss or gain of electric charge. Although charge flows between two objects during an electrostatic discharge, time is too short for current to be maintained.

 Electrification by friction

Experiment I

Let a piece of glass and a piece of resin, neither of which exhibits any electrical properties, be rubbed together and left with the rubbed surfaces in contact. They will still exhibit no electrical properties. Let them be separated. They will now attract each other.

If a second piece of glass be rubbed with a second piece of resin, and if the piece be then separated and suspended in the neighbourhood of the former pieces of glass and resin, it may be observed:

  1. that the two pieces of glass repel each other.
  2. that each piece of glass attracts each piece of resin.
  3. that the two pieces of resin repel each other.

These phenomena of attraction and repulsion are called electrical phenomena and the bodies which exhibit them are said to be 'electrified', or to be 'charged with electricity'.

Bodies may be electrified in many other ways, as well as by friction.

The electrical properties of the two pieces of glass are similar to each other but opposite to those of the two pieces of resin: the glass attracts what the resin repels and repels what the resin attracts.

If a body electrified in any manner whatever behaves as the glass does, that is, if it repels the glass and attracts the resin, the body is said to be 'vitreously' electrified, and if it attracts the glass and repels the resin it is said to be 'resinously' electrified. All electrified bodies are found to be either vitreously or resinously electrified.

It is the established convention of the scientific community to define the vitreous electrification as positive, and the resinous electrification as negative. The exactly opposite properties of the two kinds of electrification justify us in indicating them by opposite signs, but the application of the positive sign to one rather than to the other kind must be considered as a matter of arbitrary convention, just as it is a matter of convention in mathematical diagram to reckon positive distances towards the right hand.

No force, either of attraction or of repulsion, can be observed between an electrified body and a body not electrified.[3]

We now know that the Franklin/Watson model was fundamentally correct. There is only one kind of electrical charge, and only one variable is required to keep track of the amount of charge.[4] On the other hand, just knowing the charge is not a complete description of the situation. Matter is composed of several kinds of electrically charged particles, and these particles have many properties, not just charge.

The most common charge carriers are the positively charged proton and the negatively charged electron. The movement of any of these charged particles constitutes an electric current. In many situations, it suffices to speak of the conventional current without regard to whether it is carried by positive charges moving in the direction of the conventional current and/or by negative charges moving in the opposite direction. This macroscopic viewpoint is an approximation that simplifies electromagnetic concepts and calculations.

At the opposite extreme, if one looks at the microscopic situation, one sees there are many ways of carrying an electric current, including: a flow of electrons; a flow of electron "holes" which act like positive particles; and both negative and positive particles (ions or other charged particles) flowing in opposite directions in an electrolytic solution or a plasma).

Beware that in the common and important case of metallic wires, the direction of the conventional current is opposite to the drift velocity of the actual charge carriers, i.e. the electrons. This is a source of confusion for beginner.

Aside from the properties described in articles about electromagnetism, charge is a relativistic invariant. This means that any particle that has charge Q, no matter how fast it goes, always has charge Q. This property has been experimentally verified by showing that the charge of one helium nucleus (two protons and two neutrons bound together in a nucleus and moving around at high speeds) is the same as two deuterium nuclei (one proton and one neutron bound together, but moving much more slowly than they would if they were in a helium nucleus).

Conservation of electric charge

The total electric charge of an isolated system remains constant regardless of changes within the system itself. This law is inherent to all processes known to physics and can be derived in a local form from gauge invariance of the wave function. The conservation of charge results in the charge-current continuity equation. More generally, the net change in charge density ρ within a volume of integration V is equal to the area integral over the current density J through the closed surface S = ∂V, which is in turn equal to the net current I:

Thus, the conservation of electric charge, as expressed by the continuity equation, gives the result:

The charge transferred between times ti and tf is obtained by integrating both sides:

where I is the net outward current through a closed surface and Q is the electric charge contained within the volume defined by the surface.


Electric current

From Wikipedia, the free encyclopedia

Electricity · Magnetism
Ampère’s law · Electric current · Magnetic field · Magnetization · Magnetic flux · Biot–Savart law · Magnetic dipole moment · Gauss's law for magnetism

Electric current can mean, depending on the context, a flow of electric charge (a phenomenon) or the rate of flow of electric charge (a quantity).[1] This flowing electric charge is typically carried by moving electrons, in a conductor such as wire; in an electrolyte, it is instead carried by ions, and, in a plasma, by both.[2]

The SI unit for measuring the rate of flow of electric charge is the ampere. Electric current is measured using an ammeter.[1]



Electric current through various media


A solid conductive metal contains mobile, or free, electrons. These electrons are bound to the metal lattice but not to any individual atom. Even with no external electric field applied, these electrons move about randomly due to thermal energy but, on average, there is zero net current within the metal. Given a plane through which the wire passes, the number of electrons moving from one side to the other in any period of time is on average equal to the number passing in the opposite direction. As George Gamow put in his science popularizing book, One, Two, Three...Infinity (1947), "The metallic substances differ from all other materials by the fact that the outer shells of their atoms are bound rather loosely, and often let one of their electrons go free. Thus the interior of a metal is filled up with a large number of unattached electrons that travel aimlessly around like a crowd of displaced persons. When a metal wire is subjected to electric force applied on its opposite ends, these free electrons rush in the direction of the force, thus forming what we call an electric current."


When a metal wire is connected across the two terminals of a DC voltage source such as a battery, the source places an electric field across the conductor. The moment contact is made, the free electrons of the conductor are forced to drift toward the positive terminal under the influence of this field. The free electrons are therefore the current carrier in a typical solid conductor. For an electric current of 1 ampere, 1 coulomb of electric charge (which consists of about 6.242 × 1018 elementary charges) drifts every second through any plane through which the conductor passes.

For a steady flow, the current I in amperes can be calculated with the following equation:


Q is the electric charge in coulombs transferred
t is the time in seconds

More generally, electric current can be represented as the time rate of change of charge, or


Other media


In metallic solids, electricity flows by means of electrons, from higher to lower electrical potential. In other media, any stream of charged objects may constitute an electric current.So when there is higher cross sectional area there is less Resistance. Conventional currents flows in the opposite way of electron current. In terms of Ohms law Current is propotional to Voltage and Inversely propotional to the Resistance. measure in Volts and Amps.

In a vacuum, a beam of ions or electrons may be formed. In other conductive materials, the electric current is due to the flow of both positively and negatively charged particles at the same time. In still others, the current is entirely due to positive charge flow. For example, the electric currents in electrolytes are flows of electrically charged atoms (ions), which exist in both positive and negative varieties. In a common lead-acid electrochemical cell, electric currents are composed of positive hydrogen ions (protons) flowing in one direction, and negative sulfate ions flowing in the other. Electric currents in sparks or plasma are flows of electrons as well as positive and negative ions. In ice and in certain solid electrolytes, the electric current is entirely composed of flowing ions. In a semiconductor it is sometimes useful to think of the current as due to the flow of positive "holes" (the mobile positive charge carriers that are places where the semiconductor crystal is missing a valence electron). This is the case in a p-type semiconductor.

Current density

Current density is a measure of the density of an electric current. It is defined as a vector whose magnitude is the electric current per cross-sectional area. In SI units, the current density is measured in amperes per square meter.



I is current in the conductor
J is the current density, and,
A is the cross-sectional area.

The dot product of two vector quantity signifies that electric current is a scalar.

Drift speed

The mobile charged particles within a conductor move constantly in random directions, like the particles of a gas. In order for there to be a net flow of charge, the particles must also move together with an average drift rate. Electrons are the charge carriers in metals and they follow an erratic path, bouncing from atom to atom, but generally drifting in the direction of the electric field. The speed at which they drift can be calculated from the equation:

I = nAvQ


I is the electric current
n is number of charged particles per unit volume (or charge carrier density)
A is the cross-sectional area of the conductor
v is the drift velocity, and
Q is the charge on each particle.

Electric currents in solids typically flow very slowly. For example, in a copper wire of cross-section 0.5 mm2, carrying a current of 5 A, the drift velocity of the electrons is of the order of a millimetre per second. To take a different example, in the near-vacuum inside a cathode ray tube, the electrons travel in near-straight lines at about a tenth of the speed of light.

Any accelerating electric charge, and therefore any changing electric current, gives rise to an electromagnetic wave that propagates at very high speed outside the surface of the conductor. This speed is usually a significant fraction of the speed of light, as can be deduced from Maxwell's Equations, and is therefore many times faster than the drift velocity of the electrons. For example, in AC power lines, the waves of electromagnetic energy propagate through the space between the wires, moving from a source to a distant load, even though the electrons in the wires only move back and forth over a tiny distance.

The ratio of the speed of the electromagnetic wave to the speed of light in free space is called the velocity factor, and depends on the electromagnetic properties of the conductor and the insulating materials surrounding it, and on their shape and size.

The nature of these three velocities can be illustrated by an analogy with the three similar velocities associated with gases. The low drift velocity of charge carriers is analogous to air motion; in other words, winds. The high speed of electromagnetic waves is roughly analogous to the speed of sound in a gas; while the random motion of charges is analogous to heat - the thermal velocity of randomly vibrating gas particles.


According to Ampère's law, an electric current produces a magnetic field.

Electric current produces a magnetic field. The magnetic field can be visualized as a pattern of circular field lines surrounding the wire.

Electric current can be directly measured with a galvanometer, but this method involves breaking the circuit, which is sometimes inconvenient. Current can also be measured without breaking the circuit by detecting the magnetic field associated with the current. Devices used for this include Hall effect sensors, current clamps, current transformers, and Rogowski coils.

The theory of Special Relativity allows one to transform the magnetic field into a static electric field for an observer moving at the same speed as the charge in the diagram. The amount of current is particular to a reference frame (who is measuring the current or charge velocity).

Ohm's law

Ohm's law states that the current flowing in the metal is directly proportional to the potential difference between two ends(across) of that metal (ideal) resistor (or other ohmic device).i.,e,

V = IR


I is the current, measured in amperes
V is the potential difference measured in volts
R is the resistance measured in ohms


Current flow

Diagram showing conventional current notation and the flow of electrons. Electric charge moves from the positive side of the power source to the negative, while electrons move from anode to cathode.

A flow of positive charge gives the same electric current as an opposite flow of negative charge. Thus, opposite flows of opposite charges contribute to a single electric current. For this reason, the polarity of the flowing charges can usually be ignored during measurements. All the flowing charges are assumed to have positive polarity, and this flow is called conventional current. Conventional current represents the net effect of the current flow, without regard to the sign of the charge of the objects carrying the current.

In solid metals such as wires, the positive charge carriers are immobile, and only the negatively charged electrons flow. Because the electron carries negative charge, the electron motion in a metal is in the direction opposite to that of conventional (or electric) current.

Reference direction

When solving electrical circuits, the actual direction of current through a specific circuit element is usually unknown. Consequently, each circuit element is assigned a current variable with an arbitrarily chosen reference direction. When the circuit is solved, the circuit element currents may have positive or negative values. A negative value means that the actual direction of current through that circuit element is opposite that of the chosen reference direction.


Natural examples include lightning and the solar wind, the source of the polar auroras (the aurora borealis and aurora australis). The artificial form of electric current is the flow of conduction electrons in metal wires, such as the overhead power lines that deliver electrical energy across long distances and the smaller wires within electrical and electronic equipment. In electronics, other forms of electric current include the flow of electrons through resistors or through the vacuum in a vacuum tube, the flow of ions inside a battery or a neuron, and the flow of holes within a semiconductor.

Electrical safety

The most obvious hazard is electrical shock. The amount of current passing through the body, as well as the nature of the contact, the condition of the body part, the current path through the body and the voltage of the source determines the effect. While a very small amount can cause a slight tingle, large amounts can cause severe burns if it passes through the skin or even cardiac arrest if enough passes through the heart. The effect also varies considerably from individual to individual.[citation needed]

Accidental electric heating can also be dangerous. An overloaded power cable is a frequent cause of fire. A battery as small as an AA cell placed in a pocket with metal coins can lead to a short circuit heating the battery and the coins which may inflict burns. NiCad, NiMh cells, and lithium batteries are particularly risky because they can deliver a very high current due to their low internal resistance.

Electric field

From Wikipedia, the free encyclopedia

Electricity · Magnetism
Electric charge · Coulomb's law · Electric field · Electric flux · Gauss's law · Electric potential · Electrostatic induction · Electric dipole moment · Polarization density

In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. This electric field exerts a force on other electrically charged objects. The concept of an electric field was introduced by Michael Faraday.

The electric field is a vector field with SI units of newtons per coulomb (N C−1) or, equivalently, volts per metre (V m−1). The SI base units of the electric field are kg·m·s−3·A−1. The strength of the field at a given point is defined as the force that would be exerted on a positive test charge of +1 coulomb placed at that point; the direction of the field is given by the direction of that force. Electric fields contain electrical energy with energy density proportional to the square of the field intensity. The electric field is to charge as gravitational acceleration is to mass and force density is to volume.

A moving charge has not just an electric field but also a magnetic field, and in general the electric and magnetic fields are not completely separate phenomena; what one observer perceives as an electric field, another observer in a different frame of reference perceives as a mixture of electric and magnetic fields. For this reason, one speaks of "electromagnetism" or "electromagnetic fields." In quantum mechanics, disturbances in the electromagnetic fields are called photons, and the energy of photons is quantized.


A stationary charged particle in an electric field experiences a force proportional to its charge given by the equation


where the magnetic flux density is given by

and where is the Coulomb force. (See the section below).

Electric charge is a characteristic of some subatomic particles, and is quantized when expressed as a multiple of the so-called elementary charge e. Electrons by convention have a charge of −1, while protons have the opposite charge of +1. Quarks have a fractional charge of −1/3 or +2/3. The antiparticle equivalents of these have the opposite charge. Other subatomic particles carry electric charge, such as muons and tauons.

In general, same-sign charged particles repel one another, while different-sign charged particles attract. This is expressed quantitatively in Coulomb's law, which states the magnitude of the repelling force is proportional to the product of the two charges, and weakens proportionately to the square of the distance.

The electric charge of a macroscopic object is the sum of the electric charges of its constituent particles. Often, the net electric charge is zero, since naturally the number of electrons in every atom is equal to the number of the protons, so their charges cancel out. Situations in which the net charge is non-zero are often referred to as static electricity. Furthermore, even when the net charge is zero, it can be distributed non-uniformly (e.g., due to an external electric field), and then the material is said to be polarized, and the charge related to the polarization is known as bound charge (while the excess charge brought from outside is called free charge). An ordered motion of charged particles in a particular direction (in metals, these are the electrons) is known as electric current. The discrete nature of electric charge was proposed by Michael Faraday in his electrolysis experiments, then directly demonstrated by Robert Millikan in his oil-drop experiment.

The SI unit for quantity of electricity or electric charge is the coulomb, which represents approximately 6.25 × 1018 elementary charges (the charge on a single electron or proton). The coulomb is defined as the quantity of charge that has passed through the cross-section of an electrical conductor carrying one ampere within one second. The symbol Q is often used to denote a quantity of electricity or charge. The quantity of electric charge can be directly measured with an electrometer, or indirectly measured with a ballistic galvanometer.

Formally, a measure of charge should be a multiple of the elementary charge e (charge is quantized), but since it is an average, macroscopic quantity, many orders of magnitude larger than a single elementary charge, it can effectively take on any real value. Furthermore, in some contexts it is meaningful to speak of fractions of a charge; e.g. in the charging of a capacitor.

If the charged particle can be considered a point charge, the electric field is defined as the force it experiences per unit charge:


is the electric force experienced by the particle
q is its charge
is the electric field wherein the particle is located

Taken literally, this equation only defines the electric field at the places where there are stationary charges present to experience it. Furthermore, the force exerted by another charge q will alter the source distribution, which means the electric field in the presence of q differs from itself in the absence of q. However, the electric field of a given source distribution remains defined in the absence of any charges with which to interact. This is achieved by measuring the force exerted on successively smaller test charges placed in the vicinity of the source distribution. By this process, the electric field created by a given source distribution is defined as the limit as the test charge approaches zero of the force per unit charge exerted thereupon.

This allows the electric field to be dependent on the source distribution alone.

As is clear from the definition, the direction of the electric field is the same as the direction of the force it would exert on a positively-charged particle, and opposite the direction of the force on a negatively-charged particle. Since like charges repel and opposites attract (as quantified below), the electric field tends to point away from positive charges and towards negative charges.

Coulomb's law

The electric field surrounding a point charge is given by Coulomb's law:


Q is the charge of the particle creating the electric force,
r is the distance from the particle with charge Q to the E-field evaluation point,
is the unit vector pointing from the particle with charge Q to the E-field evaluation point,
is the electric constant.

Coulomb's law is actually a special case of Gauss's Law, a more fundamental description of the relationship between the distribution of electric charge in space and the resulting electric field. Gauss's law is one of Maxwell's equations, a set of four laws governing electromagnetics.

Time-varying fields

Charges do not only produce electric fields. As they move, they generate magnetic fields, and if the magnetic field changes, it generates electric fields. A changing magnetic field gives rise to an electric field,

which yields Faraday's law of induction,


indicates the curl of the electric field,
represents the vector rate of decrease of magnetic field with time.

This means that a magnetic field changing in time produces a curled electric field, possibly also changing in time. The situation in which electric or magnetic fields change in time is no longer electrostatics, but rather electrodynamics or electromagnetics.

Properties (in electrostatics)

Illustration of the electric field surrounding a positive (red) and a negative (green) charge.

According to equation (1) above, electric field is dependent on position. The electric field due to any single charge falls off as the square of the distance from that charge.

Electric fields follow the superposition principle. If more than one charge is present, the total electric field at any point is equal to the vector sum of the respective electric fields that each object would create in the absence of the others.

If this principle is extended to an infinite number of infinitesimally small elements of charge, the following formula results:


ρ is the charge density, or the amount of charge per unit volume.

The electric field at a point is equal to the negative gradient of the electric potential there. In symbols,


φ(x,y,z) is the scalar field representing the electric potential at a given point.

If several spatially distributed charges generate such an electric potential, e.g. in a solid, an electric field gradient may also be defined.

Considering the permittivity of a material, which may differ from the permittivity of free space , the electric displacement field is:

Energy in the electric field

The electric field stores energy. The energy density of the electric field is given by


            is the permittivity of the medium in which the field exists
is the electric field vector.

The total energy stored in the electric field in a given volume V is therefore


dV is the differential volume element.

Parallels between electrostatics and gravity

Coulomb's law, which describes the interaction of electric charges:

is similar to Newton's law of universal gravitation:

This suggests similarities between the electric field E and the gravitational field g, so sometimes mass is called "gravitational charge".

Similarities between electrostatic and gravitational forces:

  1. Both act in a vacuum.
  2. Both are central and conservative.
  3. Both obey an inverse-square law (both are inversely proportional to square of r).
  4. Both propagate with finite speed c.

Differences between electrostatic and gravitational forces:

  1. Electrostatic forces are much greater than gravitational forces (by about 1036 times).
  2. Gravitational forces are attractive for like charges, whereas electrostatic forces are repulsive for like charges.
  3. There are no negative gravitational charges (no negative mass) while there are both positive and negative electric charges. This difference combined with previous implies that gravitational forces are always attractive, while electrostatic forces may be either attractive or repulsive.
  4. Electric charge is invariant while relativistic mass is not.

Electric potential

From Wikipedia, the free encyclopedia

Jump to: navigation, search
Electricity · Magnetism
Electric charge · Coulomb's law · Electric field · Electric flux · Gauss's law · Electric potential · Electrostatic induction · Electric dipole moment · Polarization density

At a point in space, the electric potential (also called the "electrostatic potential") is potential energy divided by charge that is associated with a static (time-invariant) electric field. It is a scalar quantity, typically measured in volts.

There is also a generalized electric scalar potential that is used in electrodynamics when time-varying electromagnetic fields are present. This generalized electric potential cannot be simply interpreted as the ratio of potential energy to charge, however.



Objects may possess a property known as electric charge. An electric field exerts a force on charged objects, accelerating them in the direction of the force, in either the same or the opposite direction of the electric field. If the charged object has a positive charge, the force and acceleration will be in the direction of the field. This force has the same direction as the electric field vector, and its magnitude is given by the size of the charge multiplied with the magnitude of the electric field.

Classical mechanics explores the concepts such as force, energy, potential etc. in more detail.

Force and potential energy are directly related. As an object moves in the direction that the force accelerates it, its potential energy decreases. For example, the gravitational potential energy of a cannonball at the top of a hill is greater than at the base of the hill. As the object falls, that potential energy decreases and is translated to motion, or inertial (kinetic) energy.

For certain forces, it is possible to define the "potential" of a field such that the potential energy of an object due to a field is dependent only on the position of the object with respect to the field. Those forces must affect objects depending only on the intrinsic properties of the object and the position of the object, and obey certain other mathematical rules.

Two such forces are the gravitational force (gravity) and the electric force in the absence of time-varying magnetic fields. The potential of an electric field is called the electric potential. The synonymous term "electrostatic potential" is also in common use.

The electric potential and the magnetic vector potential together form a four vector, so that the two kinds of potential are mixed under Lorentz transformations.

Mathematical introduction

The concept of electric potential (denoted by: φ, φE or V) is closely linked with potential energy, thus:

UE = qφ

where UE is the electric potential energy of a test charge q due to the electric field. Note that the potential energy and hence also the electric potential is only defined up to an additive constant: one must arbitrarily choose a position where the potential energy and the electric potential is zero.

The proper definition of the electric potential uses the electric field :

where C is an arbitrary path connecting the point with zero potential to the point under consideration. When , the line integral above does not depend on the specific path C chosen but only on its endpoints. Equivalently, the electric potential determines the electric field via its gradient:

and therefore, by Gauss's law, the potential satisfies Poisson's equation:

where ρ is the total charge density (including bound charge).

Note: these equations cannot be used if , i.e., in the case of a nonconservative electric field (caused by a changing magnetic field; see Maxwell's equations). The generalization of electric potential to this case is described below.

Electric potentials due to point charges

The electric potential created by a point charge q, at a distance r from the charge (relative to the potential at infinity), can be shown to be

where ε0 is the vacuum permittivity.

The electric potential due to a system of point charges is equal to the sum of the point charges' individual potentials. This fact simplifies calculations significantly, since addition of potential (scalar) fields is much easier than addition of the electric (vector) fields.

The equation given above for the electric potential (and all the equations used here) are in the forms required by SI units. In some other (less common) systems of units, such as CGS-Gaussian, many of these equations would be altered.

Generalization to electrodynamics

When time-varying magnetic fields are present (which is true whenever there are time-varying electric fields and vice versa), one cannot describe the electric field simply in terms of a scalar potential φ; because the electric field is no longer conservative: is path-dependent because .

Instead, one can still define a scalar potential by also including the magnetic vector potential . In particular, is defined to satisfy:

where is the magnetic field. Because divergence of magnetic field is always zero due to the absence of magnetic monopoles, such an can always be found. Given this, the quantity is a conservative field by Faraday's law and one can therefore write:



The SI unit of electric potential is the volt (in honor of Alessandro Volta). Older units are rarely used nowadays. Variants of the centimeter gram second system of units included a number of different units for electric potential, including the abvolt and the statvolt.


From Wikipedia, the free encyclopedia

Electricity · Magnetism

Electromagnetism is the physics of the electromagnetic field, a field that exerts a force on particles with the property of electric charge and is reciprocally affected by the presence and motion of such particles.

A changing magnetic field produces an electric field (this is the phenomenon of electromagnetic induction, the basis of operation for electrical generators, induction motors, and transformers). Similarly, a changing electric field generates a magnetic field.

The magnetic field is produced by the motion of electric charges, i.e., electric current. The magnetic field causes the magnetic force associated with magnets.

The theoretical implications of electromagnetism led to the development of special relativity by Albert Einstein in 1905; and from this it was shown that magnetic fields and electric fields are convertible with relative motion as a four vector.




While preparing for an evening lecture on 21 April 1820, Hans Christian Ørsted made a surprising observation. As he was setting up his materials, he noticed a compass needle deflected from magnetic north when the electric current from the battery he was using was switched on and off. This deflection convinced him that magnetic fields radiate from all sides off of a wire carrying an electric current, just as light and heat do, and that it confirmed a direct relationship between electricity and magnetism.

At the time of discovery, Ørsted did not suggest any satisfactory explanation of the phenomenon, nor did he try to represent the phenomenon in a mathematical framework. However, three months later he began more intensive investigations. Soon thereafter he published his findings, proving that an electric current produces a magnetic field as it flows through a wire. The CGS unit of magnetic induction (oersted) is named in honor of his contributions to the field of electromagnetism.

His findings resulted in intensive research throughout the scientific community in electrodynamics. They influenced French physicist André-Marie Ampère's developments of a single mathematical form to represent the magnetic forces between current-carrying conductors. Ørsted's discovery also represented a major step toward a unified concept of energy.

This unification, which was observed by Michael Faraday, extended by James Clerk Maxwell, and partially reformulated by Oliver Heaviside and Heinrich Hertz, is one of the accomplishments of 19th century Mathematical Physics. It had far-reaching consequences, one of which was the understanding of the nature of light. Light and other electromagnetic waves take the form of quantized, self-propagating oscillatory electromagnetic field disturbances called photons. Different frequencies of oscillation give rise to the different forms of electromagnetic radiation, from radio waves at the lowest frequencies, to visible light at intermediate frequencies, to gamma rays at the highest frequencies.

Ørsted was not the only person to examine the relation between electricity and magnetism. In 1802 Gian Domenico Romagnosi, an Italian legal scholar, deflected a magnetic needle by electrostatic charges. Actually, no galvanic current existed in the setup and hence no electromagnetism was present. An account of the discovery was published in 1802 in an Italian newspaper, but it was largely overlooked by the contemporary scientific community.

The electromagnetic force

The force that the electromagnetic field exerts on electrically charged particles, called the electromagnetic force, is one of the fundamental forces. The other fundamental forces are strong nuclear force (which holds atomic nuclei together), the weak nuclear force and the gravitational force. All other forces (e.g. friction) are ultimately derived from these fundamental forces.

The electromagnetic force is the one responsible for practically all the phenomena encountered in daily life, with the exception of gravity. All the forces involved in interactions between atoms can be traced to the electromagnetic force acting on the electrically charged protons and electrons inside the atoms. This includes the forces we experience in "pushing" or "pulling" ordinary material objects, which come from the intermolecular forces between the individual molecules in our bodies and those in the objects. It also includes all forms of chemical phenomena, which arise from interactions between electron orbitals.

Classical electrodynamics

The scientist William Gilbert proposed, in his De Magnete (1600), that electricity and magnetism, while both capable of causing attraction and repulsion of objects, were distinct effects. Mariners had noticed that lightning strikes had the ability to disturb a compass needle, but the link between lightning and electricity was not confirmed until Benjamin Franklin's proposed experiments in 1752. One of the first to discover and publish a link between man-made electric current and magnetism was Romagnosi, who in 1802 noticed that connecting a wire across a voltaic pile deflected a nearby compass needle. However, the effect did not become widely known until 1820, when Ørsted performed a similar experiment.[1] Ørsted's work influenced Ampère to produce a theory of electromagnetism that set the subject on a mathematical foundation.

An accurate theory of electromagnetism, known as classical electromagnetism, was developed by various physicists over the course of the 19th century, culminating in the work of James Clerk Maxwell, who unified the preceding developments into a single theory and discovered the electromagnetic nature of light. In classical electromagnetism, the electromagnetic field obeys a set of equations known as Maxwell's equations, and the electromagnetic force is given by the Lorentz force law.

One of the peculiarities of classical electromagnetism is that it is difficult to reconcile with classical mechanics, but it is compatible with special relativity. According to Maxwell's equations, the speed of light in a vacuum is a universal constant, dependent only on the electrical permittivity and magnetic permeability of free space. This violates Galilean invariance, a long-standing cornerstone of classical mechanics. One way to reconcile the two theories is to assume the existence of a luminiferous aether through which the light propagates. However, subsequent experimental efforts failed to detect the presence of the aether. After important contributions of Hendrik Lorentz and Henri Poincaré, in 1905, Albert Einstein solved the problem with the introduction of special relativity, which replaces classical kinematics with a new theory of kinematics that is compatible with classical electromagnetism. (For more information, see History of special relativity.)

In addition, relativity theory shows that in moving frames of reference a magnetic field transforms to a field with a nonzero electric component and vice versa; thus firmly showing that they are two sides of the same coin, and thus the term "electromagnetism". (For more information, see Classical electromagnetism and special relativity.)

The photoelectric effect

In another paper published in that same year, Albert Einstein undermined the very foundations of classical electromagnetism. His theory of the photoelectric effect (for which he won the Nobel prize for physics) posited that light could exist in discrete particle-like quantities, which later came to be known as photons. Einstein's theory of the photoelectric effect extended the insights that appeared in the solution of the ultraviolet catastrophe presented by Max Planck in 1900. In his work, Planck showed that hot objects emit electromagnetic radiation in discrete packets, which leads to a finite total energy emitted as black body radiation. Both of these results were in direct contradiction with the classical view of light as a continuous wave, although it is now known that the photoelectric effect does not, in fact, compel one to any conclusion about light being made of "photons", as discussed in the photoelectric effect article.[citation needed] Planck's and Einstein's theories were progenitors of quantum mechanics, which, when formulated in 1925, necessitated the invention of a quantum theory of electromagnetism. This theory, completed in the 1940s, is known as quantum electrodynamics (or "QED"), and, in situations where perturbation theory is applicable, is one of the most accurate theories known to physics.


Electromagnetic units are part of a system of electrical units based primarily upon the magnetic properties of electric currents, the fundamental SI unit being the ampere. The units are:

In the electromagnetic cgs system, electrical current is a fundamental quantity defined via Ampère's law and takes the permeability as a dimensionless quantity (relative permeability) whose value in a vacuum is unity. As a consequence, the square of the speed of light appears explicitly in some of the equations interrelating quantities in this system.

SI electromagnetism units
Symbol[2] Name of Quantity Derived Units Unit Base Units
I Electric current ampere (SI base unit) A A (= W/V = C/s)
Q Electric charge coulomb C A·s
U, ΔV, Δφ; E Potential difference; Electromotive force volt V J/C = kg·m2·s−3·A−1
R; Z; X Electric resistance; Impedance; Reactance ohm Ω V/A = kg·m2·s−3·A−2
ρ Resistivity ohm metre Ω·m kg·m3·s−3·A−2
P Electric power watt W V·A = kg·m2·s−3
C Capacitance farad F C/V = kg−1·m−2·A2·s4
E Electric field strength volt per metre V/m N/C = kg·m·A−1·s−3
D Electric displacement field Coulomb per square metre C/m2 A·s·m−2
ε Permittivity farad per metre F/m kg−1·m−3·A2·s4
χe Electric susceptibility (dimensionless) - -
G; Y; B Conductance; Admittance; Susceptance siemens S Ω−1 = kg−1·m−2·s3·A2
κ, γ, σ Conductivity siemens per metre S/m kg−1·m−3·s3·A2
B Magnetic flux density, Magnetic induction tesla T Wb/m2 = kg·s−2·A−1 = N·A−1·m−1
Φ Magnetic flux weber Wb V·s = kg·m2·s−2·A−1
H Magnetic field strength ampere per metre A/m A·m−1
L, M Inductance henry H Wb/A = V·s/A = kg·m2·s−2·A−2
μ Permeability henry per metre H/m kg·m·s−2·A−2
χ Magnetic susceptibility (dimensionless) - -

Electromagnetic phenomena

With the exception of gravitation, electromagnetic phenomena as described by quantum electrodynamics (which includes as a limiting case classical electrodynamics) account for almost all physical phenomena observable to the unaided human senses, including light and other electromagnetic radiation, all of chemistry, most of mechanics (excepting gravitation), and of course magnetism and electricity. Magnetic electricity is not strictly an electromagnetic phenomena, as the principles and behavior of magnetic monopoles are more similar to the principles of electricity. Magnetricity is only known to occur in exotic materials(spin ice) combined in the laboratory.[3]