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### Energy

1. 1. {EnergyPrepared By Engr. Ahmad Sameer NawabKardan University Kabul, Afghanistan
2. 2.  Thomas Young – the first to use the term "energy" in the modern sense. The concept of energy emerged out of the idea of vis viva (living force), which GottfriedLeibniz defined as the product of the mass of an object and its velocity squared; hebelieved that total vis viva was conserved. To account for slowing due to friction,Leibniz theorized that thermal energy consisted of the random motion of theconstituent parts of matter, a view shared by Isaac Newton, although it would be morethan a century until this was generally accepted. In 1807, Thomas Young was possiblythe first to use the term "energy" instead of vis viva, in its modern sense.Gustave-Gaspard Coriolis described "kinetic energy" in 1829 in its modern sense, and in 1853,William Rankine coined the term "potential energy". It was argued for some yearswhether energy was a substance (the caloric) or merely a physical quantity, such asmomentum.History
3. 3.  There is a fact, or if you wish, a law, governing all natural phenomena that are known todate. There is no known exception to this law—it is exact so far as we know. The law iscalled the conservation of energy. It states that there is a certain quantity, which we callenergy, that does not change in manifold changes which nature undergoes. That is amost abstract idea, because it is a mathematical principle; it says that there is a numericalquantity which does not change when something happens. It is not a description of amechanism, or anything concrete; it is just a strange fact that we can calculate somenumber and when we finish watching nature go through her tricks and calculate thenumber again, it is the same. —The Feynman Lectures on Physics Since 1918 it has been known that the law of conservation of energy is the directmathematical consequence of the translational symmetry of the quantity conjugate toenergy, namely time. That is, energy is conserved because the laws of physics do notdistinguish between different instants of time (see Noethers theorem). William Thomson (Lord Kelvin) amalgamated all of these laws into the laws ofthermodynamics, which aided in the rapid development of explanations of chemicalprocesses by Rudolf Clausius, Josiah Willard Gibbs, and Walther Nernst. It also led to amathematical formulation of the concept of entropy by Clausius and to the introductionof laws of radiant energy by Jožef Stefan. During a 1961 lecture.for undergraduate students at the California Institute ofTechnology, Richard Feynman, a celebrated physics teacher and Nobel Laureate, saidthis about the concept of energy:History
4. 4.  In Physics, energy (Ancient Greek)ἐνέργεια Engergia ("activity,operation") is an indirectly observed quantity that is often understood asthe ability of a Physical Systdem to do Work on other physical systems. Since work is defined as a Force acting through a distance (a length ofspace), energy is always equivalent to the ability to exert pulls or pushesagainst the basic forces of nature, along a path of a certain length.The total energy contained in an object is identified with its Mass, andenergy (like mass), cannot be created or destroyed. When Matter(ordinary material particles) is changed into energy (such as energy ofmotion, or into radiation), the mass of the system does not changethrough the transformation process.Energy, like mass, is a Scalar physical quantity International System OFUnits (SI), energy is measured in Joules, but in many fields other units,such as kilowatt-hours and kilocalories, are customary. All of these unitstranslate to units of work, which is always defined in terms of forces andthe distances that the forces act through.What IS Energy
5. 5.  A system can transfer energy to another system by simply transferringmatter to it (since matter is equivalent to energy, in accordance with itsmass).However, when energy is transferred by means other than matter-transfer, the transfer produces changes in the second system, as a result ofwork done on it. This work manifests itself as the effect of force(s) applied throughdistances within the target system. For example, a system can emit energyto another by transferring (radiating) electromagnetic energy, but thiscreates forces upon the particles that absorb the radiation. Similarly, a system may transfer energy to another by physicallyimpacting it, but in that case the energy of motion in an object, calledkinetic energy, results in forces acting over distances (new energy) toappear in another object that is struck. Transfer of thermal energy by heat occurs by both of these mechanisms:heat can be transferred by electromagnetic radiation, or by physicalcontact in which direct particle-particle impacts transfer kinetic energy.Transformation OF Energy
6. 6.  The energy "stored" by force-fields and particles that have been forced into a newphysical configuration in the field by doing work on them by another system, isreferred to as potential energy. A simple example of potential energy is the work neededto lift an object in a gravity field, up to a support. Each of the basic forces of nature isassociated with a different type of potential energy, and all types of potential energy(like all other types of energy) appears as system mass, whenever present. For example,a compressed spring will be slightly more massive than before it was compressed.Likewise, whenever energy is transferred between systems by any mechanism, anassociated mass is transferred with it. Any form of energy may be transformed into another form. For example, all types ofpotential energy are converted into kinetic energy when the objects are given freedomto move to different position (as for example, when an object falls off a support). Whenenergy is in a form other than thermal energy, it may be transformed with good or evenperfect efficiency, to any other type of energy, including electricity or production of newparticles of matter. With thermal energy, however, there are often limits to the efficiencyof the conversion to other forms of energy, as described by the second law ofthermodynamics.Transformation OF Energy
7. 7.  In all such energy transformation processes, the total energy remains the same, and atransfer of energy from one system to another, results in a loss to compensate for anygain. This principle, the conservation of energy, was first postulated in the early 19thcentury, and applies to any isolated system. According to Noethers theorem, theconservation of energy is a consequence of the fact that the laws of physics do notchange over time. Although the total energy of a system does not change with time, its value may dependon the frame of reference. For example, a seated passenger in a moving airplane haszero kinetic energy relative to the airplane, but non-zero kinetic energy (and highertotal energy) relative to the Earth. Energy gives rise to weight when it is trapped in a system with zero momentum,where it can be weighed. It is also equivalent to mass, and this mass is alwaysassociated with it. Mass is also equivalent to a certain amount of energy, and likewisealways appears associated with it, as described in mass-energy equivalence. Theformula E = mc², derived by Albert Einstein (1905) quantifies the relationship betweenrest-mass and rest-energy within the concept of special relativity. In differenttheoretical frameworks, similar formulas were derived by J. J. Thomson (1881), HenriPoincaré (1900), Friedrich Hasenöhrl (1904) and othersTransformation OF Energy
8. 8.  In the context of physical sciences, several forms of energy have been defined. Theseinclude: Thermal energy, thermal energy in transit is called heat Chemical energy Electric energy Radiant energy, the energy of electromagnetic radiation Nuclear energy Magnetic energy Elastic energy Sound energy Mechanical energy Luminous energy Mass (E=mc²) These forms of energy may be divided into two main groups; kinetic energyand potential energy. Other familiar types of energy are a varying mix of both potentialand kinetic energy. Energy may be transformed between these forms, some with 100% energy conversionefficiency and others with less. Items that transform between these forms are calledtransducers. The above list of the known possible forms of energy is not necessarily complete.Whenever physical scientists discover that a certain phenomenon appears to violate thelaw of energy conservation, new forms may be added, as is the case with dark energy, ahypothetical form of energy that permeates all of space and tends to increase the rate ofexpansion of the universe.Forms OF Energy
9. 9.  Classical mechanics distinguishes between potential energy, which is a function of theposition of an object, and kinetic energy, which is a function of its movement. Bothposition and movement are relative to a frame of reference, which must be specified:this is often (and originally) an arbitrary fixed point on the surface of the Earth, theterrestrial frame of reference. It has been attempted to categorize all forms of energy aseither kinetic or potential: this is not incorrect, but neither is it clear that it is a realsimplification, as Feynman points out: These notions of potential and kinetic energy depend on a notion of length scale. Forexample, one can speak of macroscopic potential and kinetic energy, which do notinclude thermal potential and kinetic energy. Also what is called chemical potentialenergy is a macroscopic notion, and closer examination shows that it is really the sumof the potential and kinetic energy on the atomic and subatomic scale. Similar remarksapply to nuclear "potential" energy and most other forms of energy. This dependenceon length scale is non-problematic if the various length scales are decoupled, as isoften the case ... but confusion can arise when different length scales are coupled, forinstance when friction converts macroscopic work into microscopic thermal energy.Forms OF Energy
10. 10.  Imperial system Before SI units were widely adopted around the world, the British systems of English units and later imperialunits were used in Britain, the Commonwealth and the United States. The system came to be known as UnitedStates customary units in the United States and is still in use there and in a few Caribbean countries. Thesevarious systems of measurement have at times been called foot-pound-second systems after the Imperial units forlength, weight and time even though the tons, hundredweights, gallons, and nautical miles, for example, aredifferent for the U.S. units. Many Imperial units remain in use in Britain which has officially partially switchedto the SI system. Road signs are still in miles, yards, miles per hour; milk, beer and cider are sold by the pint;people measure their height in feet and inches and their weight in stone and pounds, to give just a fewexamples. Imperial units are used in many other places, for example, in many Commonwealth countries thatare considered metricated, land area is measured in acres and floor space in square feet, particularly forcommercial transactions (rather than government statistics). Similarly, gasoline is sold by the gallon in manycountries that are considered metricated. Metric system The metric system is a decimal system of measurement based on its units for length, the metre and for mass,the kilogram. It exists in several variations, with different choices of base units, though these do not affect itsday-to-day use. Since the 1960s, the International System of Units (SI) is the internationally recognized metricsystem. Metric units of mass, length, and electricity are widely used around the world for both everyday andscientific purposes. The metric system features a single base unit for many physical quantities. Other quantities are derived fromthe standard SI units. Multiples and fractions of the units are expressed as Powers of 10 of each unit. Unitconversions are always simple because they are in the ratio of ten, one hundred, one thousand, etc., so thatconvenient magnitudes for measurements are achieved by simply moving the decimal place: 1.234 metres is1234 millimetres or 0.001234 kilometres. The use of fractions, such as 2/5 of a metre, is not prohibited, butuncommon. All lengths and distances, for example, are measured in metres, or thousandths of a metre(millimetres), or thousands of metres (kilometres). There is no profusion of different units with differentconversion factors as in the Imperial system which uses, for example, inches, feet, yards, fathoms, rods.Units And Measurements
11. 11.  The International System of Units (abbreviated as SI from the Frenchlanguage name Système International dUnités) is the modern revision ofthe metric system. It is the worlds most widely used system of units, bothin everyday commerce and in science. The SI was developed in 1960 fromthe metre-kilogram-second (MKS) system, rather than the centimetre-gram-second (CGS) system, which, in turn, had many variants. During itsdevelopment the SI also introduced several newly named units that werepreviously not a part of the metric system. The original SI units for the sixbasic physical quantities were:Units And MeasurementsUnit Abbreviation Quantity measuredMetre m lengthsecond s timekilogram kg massampere A electric currentkelvin K thermodynamic temperaturecandela cd luminous intensity
12. 12. Because energy is defined via work, the SI unit for energy is the same as the unit of work –the joule (J), named in honor of James Prescott Joule and his experiments on themechanical equivalent of heat. In slightly more fundamental terms, 1 joule is equal to1 newton-metre and, in terms of SI base units: An energy unit that is used in atomic physics, particle physics and high energy physicsis the electronvolt (eV). One EV is equivalent to 1.60217653×10−19 J. In spectroscopy theunit cm−1 = 0.000123986 EV is used to represent energy since energy is inverselyproportional to wavelength from the equation . In discussions of energy production and consumption, the units barrel of oil equivalentand ton of oil equivalent are often used. When discussing amounts of energy released in explosions or bolide impact events, theTNT equivalent unit is often used. 1 ton of TNT equivalent is equal to 4.2 × 109 joules.Therefore, 1 kt TNT is 4.2 × 1012 joules, and 1 Mt TNT is 4.2 × 1015 joules. Note that torque, the "rotational force" or "angular force" which causes a change inrotational motion is typically expressed in newton-metres. This is not a simplecoincidence: a torque of 1 newton-metre applied on 1 radian requires exactly 1 newton-metre = 1 joule of energy.Units And Measurements
13. 13.  The mole, the unit of amount of substance, was subsequently added tothis list and the degree Kelvin renamed the kelvin. There are two types of SI units, base units and derived units. Base unitsare the simple measurements for time, length, mass, temperature,amount of substance, electric current and light intensity. Derived unitsare constructed from the base units, for example, the watt, i.e. the unit forpower, is defined from the base units as m2·kg·s−3. Other physicalproperties may be measured in compound units, such as material density,measured in kg·m-3.Units And Measurements
14. 14.  In cgs units, one erg is 1 gcm2 s−2, equal to 1.0×10−7 J. US units The imperial/U.S. units for both energy and work include the foot-pound force (1.3558 J),the British thermal unit (Btu) which has various values in the region of 1055 J, and thehorsepower-hour (2.6845 MJ). Electricity The energy unit used for everyday electricity, particularly for utility bills, is the kilowatt-hour (kWh), and one kWh is equivalent to 3.6×106 J (3600 kJ or 3.6 MJ). Electricity usage isoften given in units of kilowatt-hours per year (kWh/yr). This is actually a measurement ofaverage power consumption, i.e., the average rate at which energy is transferred. Food industry The calorie equals the amount of thermal energy necessary to raise the temperature of onegram of water by 1 Celsius degree, at a pressure of 1 atm. For thermochemistry a calorie of4.184 J is used, but other calories have also been defined, such as the International SteamTable calorie of 4.1868 J. Food energy is measured in large calories or kilocalories, oftensimply written capitalized as "Calories" (= 103 calories). Atom physics and chemistry In physics and chemistry, it is still common to measure energy on the atomic scale in thenon-SI, but convenient, units electronvolts (eV). The Hartree (the atomic unit of energy) iscommonly used in calculations. Historically Rydberg units have been used.Other Units Of Energy
15. 15.  Spectroscopy In spectroscopy and related fields it is common to measure energy levels in unitsof reciprocal centimetres. These units (cm−1) are strictly speaking not energyunits but units proportional to energies, with hc being the proportionalityconstant. Explosions A gram of TNT releases 980–1100 calories upon explosion. To define the tonne ofTNT, this was arbitrarily standardized by letting 1000 thermochemical calories =1 gram TNT = 4184 J (exactly).Other Units Of Energy
16. 16. When calculating kinetic energy (work to accelerate a mass from zero speed to some finitespeed) relativistically - using Lorentz transformations instead of Newtonian mechanics,Einstein discovered an unexpected by-product of these calculations to be an energy termwhich does not vanish at zero speed. He called it rest mass energy - energy which every massmust possess even when being at rest. The amount of energy is directly proportional to themass of body: Where m is the mass, c is the speed of light in vacuum, E is the rest mass energy. For example, consider electron-positron annihilation, in which the rest mass of individualparticles is destroyed, but the inertia equivalent of the system of the two particles (itsinvariant mass) remains (since all energy is associated with mass), and this inertia andinvariant mass is carried off by photons which individually are massless, but as a systemretain their mass. This is a reversible process - the inverse process is called pair creation - inwhich the rest mass of particles is created from energy of two (or more) annihilatingphotons. In this system the matter (electrons and positrons) is destroyed and changed tonon-matter energy (the photons). However, the total system mass and energy do notchange during this interaction. In general relativity, the stress-energy tensor serves as the source term for the gravitationalfield, in rough analogy to the way mass serves as the source term in the non-relativisticNewtonian approximation. It is not uncommon to hear that energy is "equivalent" to mass. It would be more accurateto state that every energy has an inertia and gravity equivalent, and because mass is a formof energy, then mass too has inertia and gravity associated with it.Relativity
17. 17.  Any living organism relies on an external source of energy—radiation from the Sun in the case of green plants;chemical energy in some form in the case of animals—to be able to grow and reproduce. The daily 1500–2000 Calories (6–8 MJ) recommended for a human adult are taken as a combination of oxygen and foodmolecules, the latter mostly carbohydrates and fats, of which glucose (C6H12O6) and stearin (C57H110O6) areconvenient examples. The food molecules are oxidised to carbon dioxide and water in the mitochondria C6H12O6 + 6O2 → 6CO2 + 6H2O C57H110O6 + 81.5O2 → 57CO2 + 55H2O and some of the energy is used to convert ADP into ATP ADP + HPO42− → ATP + H2O The rest of the chemical energy in the carbohydrate or fat is converted into heat: the ATP is used as a sort of"energy currency", and some of the chemical energy it contains when split and reacted with water, is used forother metabolism (at each stage of a metabolic pathway, some chemical energy is converted into heat). Only atiny fraction of the original chemical energy is used for work:[18] gain in kinetic energy of a sprinter during a 100 m race: 4 kJ gain in gravitational potential energy of a 150 kg weight lifted through 2 metres: 3kJ Daily food intake of a normal adult: 6–8 MJ It would appear that living organisms are remarkably inefficient (in the physical sense) in their use of theenergy they receive (chemical energy or radiation), and it is true that most real machines manage higherefficiencies. In growing organisms the energy that is converted to heat serves a vital purpose, as it allows theorganism tissue to be highly ordered with regard to the molecules it is built from. The second law ofthermodynamics states that energy (and matter) tends to become more evenly spread out across the universe:to concentrate energy (or matter) in one specific place, it is necessary to spread out a greater amount of energy(as heat) across the remainder of the universe ("the surroundings"). Simpler organisms can achieve higherenergy efficiencies than more complex ones, but the complex organisms can occupy ecological niches that arenot available to their simpler brethren. The conversion of a portion of the chemical energy to heat at each stepin a metabolic pathway is the physical reason behind the pyramid of biomass observed in ecology: to take justthe first step in the food chain, of the estimated 124.7 Pg/a of carbon that is fixed by photosynthesis, 64.3 Pg/a(52%) are used for the metabolism of green plants, i.e. reconverted into carbon dioxide and heat.Energy And Life
18. 18.  Energy density is a term used for the amount of useful energystored in a given system or region of space per unit volume. For fuels, the energy per unit volume is sometimes a usefulparameter. In a few applications, comparing, for example, theeffectiveness of hydrogen fuel to gasoline it turns out that hydrogenhas a higher specific energy than does gasoline, but, even in liquidform, a much lower energy density.Energy Density
19. 19.  The kinetic energy of an object is the energy which it possesses due to its motion.It isdefined as the work needed to accelerate a body of a given mass from rest to its statedvelocity. Having gained this energy during its acceleration, the body maintains this kineticenergy unless its speed changes. The same amount of work is done by the body indecelerating from its current speed to a state of rest. The speed, and thus the kinetic energy of a single object is frame-dependent (relative): it cantake any non-negative value, by choosing a suitable inertial frame of reference. For example,a bullet passing an observer has kinetic energy in the reference frame of this observer. Thesame bullet is stationary from the point of view of an observer moving with the samevelocity as the bullet, and so has zero kinetic energy. By contrast, the total kinetic energy of asystem of objects cannot be reduced to zero by a suitable choice of the inertial referenceframe, unless all the objects have the same velocity. In any other case the total kinetic energyhas a non-zero minimum, as no inertial reference frame can be chosen in which all the objectsare stationary. This minimum kinetic energy contributes to the systems invariant mass,which is independent of the reference frame. In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at aspeed v is ½ mv². In relativistic mechanics, this is only a good approximation when v is muchless than the speed of light.Kinetic Energy
20. 20.  Kinetic energy of rigid bodies In classical mechanics, the kinetic energy of a point object (an object so small that its mass can be assumed to existat one point), or a non-rotating rigid body depends on the mass of the body as well as its speed. The kineticenergy is equal to the mass multiplied by the square of the speed, multiplied by the constant 1/2. In formulaform: where is the mass and is the speed (or the velocity) of the body. In SI units (used for most modern scientificwork), mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules. For example, one would calculate the kinetic energy of an 80 kg mass (about 180 lbs) traveling at 18 metres persecond (about 40 mph, or 65 km/h) as Ek = (1/2) · 80 · 182 J = 12.96 kJ When you throw a ball, you do work on it to give it speed as it leaves your hand. The moving ball can then hitsomething and push it, doing work on what it hits. The kinetic energy of a moving object is equal to the workrequired to bring it from rest to that speed, or the work the object can do while being brought to rest: Net force xdistance = kinetic energy. Or, in equation notation: Since the kinetic energy increases with the square of the speed, an object doubling its speed has four times asmuch kinetic energy. For example, a car traveling twice as fast as another requires four times as much distanceto stop, assuming a constant braking force. As a consequence of this quadrupling, it takes four times the work todouble the speed. The kinetic energy of an object is related to its momentum by the equation: where: Momentum is mass of the body. For the translational kinetic energy, that is the kinetic energy associated with rectilinear motion, of a rigid bodywith constant mass , whose center of mass is moving in a straight line with speed , as seen above is equal to where: the mass of the body is the speed of the center of mass of the body.Newtonian Kinetic Energy
21. 21.  The kinetic energy of any entity depends on the reference frame in which it is measured.However the total energy of an isolated system, i.e. one which energy can neither enter norleave, does not change in whatever reference frame it is measured. Thus, the chemical energyconverted to kinetic energy by a rocket engine is divided differently between the rocket ship andits exhaust stream depending upon the chosen reference frame. This is called the Oberth effect.But the total energy of the system, including kinetic energy, fuel chemical energy, heat, etc., isconserved over time, regardless of the choice of reference frame. Different observers movingwith different reference frames disagree on the value of this conserved energy. The kinetic energy of such systems depends on the choice of reference frame: the reference framethat gives the minimum value of that energy is the center of momentum frame, i.e. the referenceframe in which the total momentum of the system is zero. This minimum kinetic energycontributes to the invariant mass of the system as a whole.Newtonian Kinetic Energy
22. 22.  In physics, potential energy is the energy of a body or a system due to theposition of the body or the arrangement of the particles of the system.The SIunit for measuring work and energy is the Joule (symbol J). The term "potential energy" was coined by the 19th century Scottish engineerand physicist William Rankine,although it has links to Greek philosopherAristotles concept of potentiality.Potential Energy
23. 23.  However, over large variations in distance, the approximation that g is constant is nolonger valid, and we have to use calculus and the general mathematical definition ofwork to determine gravitational potential energy. For the computation of the potentialenergy we can integrate the gravitational force, whose magnitude is given byNewtons law of gravitation, with respect to the distance r between the two bodies.Using that definition, the gravitational potential energy of a system of masses m1 andM2 at a distance r using gravitational constant G is Given this formula for U, the total potential energy of a system of n bodies is found bysumming, for all pairs of two bodies, the potential energy of the system of those two bodies. Gravitational potential summation Considering the system of bodies as the combined set of small particles the bodiesconsist of, and applying the previous on the particle level we get the negativegravitational binding energy. This potential energy is more strongly negative than thetotal potential energy of the system of bodies as such since it also includes thenegative gravitational binding energy of each body. The potential energy of thesystem of bodies as such is the negative of the energy needed to separate the bodiesfrom each other to infinity, while the gravitational binding energy is the energyneeded to separate all particles from each other to infinity. There fore ,General Formula
24. 24.  Elastic potential energy Calculation of elastic potential energy The elastic potential energy stored in a stretched spring can be calculated byfinding the work necessary to stretch the spring a distance x from its un-stretched length: an ideal spring will follow Hookes Law: The work done (and therefore the stored potential energy) will then be: The units are in Joules. The equation is often used in calculations of positions of mechanicalequilibrium. More involved calculations can be found at elastic potentialenergy.Kinds Of Potential Energy
25. 25.  The elastic potential energy stored in a stretched spring can becalculated by finding the work necessary to stretch the spring adistance x from its un-stretched length: an ideal spring will follow Hookes Law: The work done (and therefore the stored potential energy) willthen be:Calculation OF Elastic Potential Energy
26. 26.  Chemical potential energy is a form of potential energy related tothe structural arrangement of atoms or molecules. This arrangementmay be the result of chemical bonds within a molecule or otherwise.Chemical energy of a chemical substance can be transformed toother forms of energy by a chemical reaction. As an example, whena fuel is burned the chemical energy is converted to heat, same is thecase with digestion of food metabolized in a biological organism.Green plants transform solar energy to chemical energy through theprocess known as photosynthesis, and electrical energy can beconverted to chemical energy through electrochemical reactions. The similar term chemical potential is used to indicate the potentialof a substance to undergo a change of configuration, be it in theform of a chemical reaction, spatial transport, particle exchange witha reservoir, etc.Chemical potential Energy
27. 27.  An object can have potential energy by virtue of its electric chargeand several forces related to their presence. There are two maintypes of this kind of potential energy: electrostatic potential energy,electro dynamic potential energy (also sometimes called magneticpotential energy). Plasma formed inside a gas filled sphereElectrical Potential Energy
28. 28.  In case the electric charge of an object can be assumed to be at rest, it haspotential energy due to its position relative to other charged objects. The electrostatic potential energy is the energy of an electrically chargedparticle (at rest) in an electric field. It is defined as the work that must be doneto move it from an infinite distance away to its present location, in the absenceof any non-electrical forces on the object. This energy is non-zero if there isanother electrically charged object nearby. The simplest example is the case of two point-like objects A1 and A2 withelectrical charges q1 and q2. The work W required to move A1 from an infinitedistance to a distance r away from A2 is given by: where ε0 is the electric constant. This equation is obtained by integrating the Coulomb force between the limitsof infinity and r. A related quantity called electric potential (commonly denoted with a V forvoltage) is equal to the electric potential energy per unit charge.Electro Static Potential Energy
29. 29.  The energy of a magnetic moment m in an externally produced magnetic B-field B has potential energy The magnetization M in a field is where the integral can be over all space or, equivalently, where M is nonzero. Magnetic potential energy is the form of energy related not only tothe distance between magnetic materials, but also to the orientation, oralignment, of those materials within the field. For example, the needle of acompass has the lowest magnetic potential energy when it is aligned withthe north and south poles of the Earths magnetic field. If the needle ismoved by an outside force, torque is exerted on the magnetic dipole of theneedle by the Earths magnetic field, causing it to move back intoalignment. The magnetic potential energy of the needle is highest when it isperpendicular to the Earths magnetic field. Two magnets will havepotential energy in relation to each other and the distance between them,but this also depends on their orientation. If the opposite poles are heldapart, the potential energy will be the highest when they are near the edgeof their attraction, and the lowest when they pull together. Conversely, likepoles will have the highest potential energy when forced together, and thelowest when they spring apart.Magnetic Potential Energy
30. 30.  Nuclear potential energy is the potential energy of the particles inside anatomic nucleus. The nuclear particles are bound together by the strongnuclear force. Weak nuclear forces provide the potential energy for certainkinds of radioactive decay, such as beta decay. Nuclear particles like protons and neutrons are not destroyed in fission andfusion processes, but collections of them have less mass than if they wereindividually free, and this mass difference is liberated as heat and radiationin nuclear reactions (the heat and radiation have the missing mass, but itoften escapes from the system, where it is not measured). The energy fromthe Sun is an example of this form of energy conversion. In the Sun, theprocess of hydrogen fusion converts about 4 million tones of solar matterper second into electromagnetic energy, which is radiated into space.Nuclear Potential Energy