Energy

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Energy
Prepared By Engr. Ahmad Sameer Nawab
Kardan University Kabul, Afghanistan

 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 Gottfried
Leibniz defined as the product of the mass of an object and its velocity squared; he
believed that total vis viva was conserved. To account for slowing due to friction,
Leibniz theorized that thermal energy consisted of the random motion of the
constituent parts of matter, a view shared by Isaac Newton, although it would be more
than a century until this was generally accepted. In 1807, Thomas Young was possibly
the 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 years
whether energy was a substance (the caloric) or merely a physical quantity, such as
momentum.
History

 There is a fact, or if you wish, a law, governing all natural phenomena that are known to
date. There is no known exception to this law—it is exact so far as we know. The law is
called the conservation of energy. It states that there is a certain quantity, which we call
energy, that does not change in manifold changes which nature undergoes. That is a
most abstract idea, because it is a mathematical principle; it says that there is a numerical
quantity which does not change when something happens. It is not a description of a
mechanism, or anything concrete; it is just a strange fact that we can calculate some
number and when we finish watching nature go through her tricks and calculate the
number 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 direct
mathematical consequence of the translational symmetry of the quantity conjugate to
energy, namely time. That is, energy is conserved because the laws of physics do not
distinguish between different instants of time (see Noether's theorem).
 William Thomson (Lord Kelvin) amalgamated all of these laws into the laws of
thermodynamics, which aided in the rapid development of explanations of chemical
processes by Rudolf Clausius, Josiah Willard Gibbs, and Walther Nernst. It also led to a
mathematical formulation of the concept of entropy by Clausius and to the introduction
of laws of radiant energy by Jožef Stefan.
 During a 1961 lecture.for undergraduate students at the California Institute of
Technology, Richard Feynman, a celebrated physics teacher and Nobel Laureate, said
this about the concept of energy:
History

 In Physics, energy (Ancient Greek)ἐνέργεια Engergia ("activity,
operation") is an indirectly observed quantity that is often understood as
the 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 of
space), energy is always equivalent to the ability to exert pulls or pushes
against the basic forces of nature, along a path of a certain length.

The total energy contained in an object is identified with its Mass, and
energy (like mass), cannot be created or destroyed. When Matter
(ordinary material particles) is changed into energy (such as energy of
motion, or into radiation), the mass of the system does not change
through the transformation process.

Energy, like mass, is a Scalar physical quantity International System OF
Units (SI), energy is measured in Joules, but in many fields other units,
such as kilowatt-hours and kilocalories, are customary. All of these units
translate to units of work, which is always defined in terms of forces and
the distances that the forces act through.
What IS Energy

 A system can transfer energy to another system by simply transferring
matter to it (since matter is equivalent to energy, in accordance with its
mass).
However, when energy is transferred by means other than matter-
transfer, the transfer produces changes in the second system, as a result of
work done on it.
 This work manifests itself as the effect of force(s) applied through
distances within the target system. For example, a system can emit energy
to another by transferring (radiating) electromagnetic energy, but this
creates forces upon the particles that absorb the radiation.
 Similarly, a system may transfer energy to another by physically
impacting it, but in that case the energy of motion in an object, called
kinetic energy, results in forces acting over distances (new energy) to
appear 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 physical
contact in which direct particle-particle impacts transfer kinetic energy.
Transformation OF Energy

 The energy "stored" by force-fields and particles that have been forced into a new
physical configuration in the field by doing work on them by another system, is
referred to as potential energy. A simple example of potential energy is the work needed
to lift an object in a gravity field, up to a support. Each of the basic forces of nature is
associated 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, an
associated mass is transferred with it.
 Any form of energy may be transformed into another form. For example, all types of
potential energy are converted into kinetic energy when the objects are given freedom
to move to different position (as for example, when an object falls off a support). When
energy is in a form other than thermal energy, it may be transformed with good or even
perfect efficiency, to any other type of energy, including electricity or production of new
particles of matter. With thermal energy, however, there are often limits to the efficiency
of the conversion to other forms of energy, as described by the second law of
thermodynamics.

 In all such energy transformation processes, the total energy remains the same, and a
transfer of energy from one system to another, results in a loss to compensate for any
gain. This principle, the conservation of energy, was first postulated in the early 19th
century, and applies to any isolated system. According to Noether's theorem, the
conservation of energy is a consequence of the fact that the laws of physics do not
change over time.
 Although the total energy of a system does not change with time, its value may depend
on the frame of reference. For example, a seated passenger in a moving airplane has
zero kinetic energy relative to the airplane, but non-zero kinetic energy (and higher
total 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 always
associated with it. Mass is also equivalent to a certain amount of energy, and likewise
always appears associated with it, as described in mass-energy equivalence. The
formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between
rest-mass and rest-energy within the concept of special relativity. In different
theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri
Poincaré (1900), Friedrich Hasenöhrl (1904) and others

 In the context of physical sciences, several forms of energy have been defined. These
include:
 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 energy
and potential energy. Other familiar types of energy are a varying mix of both potential
and kinetic energy.
 Energy may be transformed between these forms, some with 100% energy conversion
efficiency and others with less. Items that transform between these forms are called
transducers.
 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 the
law of energy conservation, new forms may be added, as is the case with dark energy, a
hypothetical form of energy that permeates all of space and tends to increase the rate of
expansion of the universe.
Forms OF Energy

 Classical mechanics distinguishes between potential energy, which is a function of the
position of an object, and kinetic energy, which is a function of its movement. Both
position 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, the
terrestrial frame of reference. It has been attempted to categorize all forms of energy as
either kinetic or potential: this is not incorrect, but neither is it clear that it is a real
simplification, as Feynman points out:
 These notions of potential and kinetic energy depend on a notion of length scale. For
example, one can speak of macroscopic potential and kinetic energy, which do not
include thermal potential and kinetic energy. Also what is called chemical potential
energy is a macroscopic notion, and closer examination shows that it is really the sum
of the potential and kinetic energy on the atomic and subatomic scale. Similar remarks
apply to nuclear "potential" energy and most other forms of energy. This dependence
on length scale is non-problematic if the various length scales are decoupled, as is
often the case ... but confusion can arise when different length scales are coupled, for
instance when friction converts macroscopic work into microscopic thermal energy.
Forms OF Energy

 Imperial system
 Before SI units were widely adopted around the world, the British systems of English units and later imperial
units were used in Britain, the Commonwealth and the United States. The system came to be known as United
States customary units in the United States and is still in use there and in a few Caribbean countries. These
various systems of measurement have at times been called foot-pound-second systems after the Imperial units for
length, weight and time even though the tons, hundredweights, gallons, and nautical miles, for example, are
different for the U.S. units. Many Imperial units remain in use in Britain which has officially partially switched
to 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 few
examples. Imperial units are used in many other places, for example, in many Commonwealth countries that
are considered metricated, land area is measured in acres and floor space in square feet, particularly for
commercial transactions (rather than government statistics). Similarly, gasoline is sold by the gallon in many
countries 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 its
day-to-day use. Since the 1960s, the International System of Units (SI) is the internationally recognized metric
system. Metric units of mass, length, and electricity are widely used around the world for both everyday and
scientific purposes.
 The metric system features a single base unit for many physical quantities. Other quantities are derived from
the standard SI units. Multiples and fractions of the units are expressed as Powers of 10 of each unit. Unit
conversions are always simple because they are in the ratio of ten, one hundred, one thousand, etc., so that
convenient magnitudes for measurements are achieved by simply moving the decimal place: 1.234 metres is
1234 millimetres or 0.001234 kilometres. The use of fractions, such as 2/5 of a metre, is not prohibited, but
uncommon. 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 different
conversion factors as in the Imperial system which uses, for example, inches, feet, yards, fathoms, rods.
Units And Measurements

 The International System of Units (abbreviated as SI from the French
language name Système International d'Unités) is the modern revision of
the metric system. It is the world's most widely used system of units, both
in everyday commerce and in science. The SI was developed in 1960 from
the metre-kilogram-second (MKS) system, rather than the centimetre-
gram-second (CGS) system, which, in turn, had many variants. During its
development the SI also introduced several newly named units that were
previously not a part of the metric system. The original SI units for the six
basic physical quantities were:
Unit Abbreviation Quantity measured
Metre m length
second s time
kilogram kg mass
ampere A electric current
kelvin K thermodynamic temperature
candela cd luminous intensity

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 the
mechanical equivalent of heat. In slightly more fundamental terms, 1 joule is equal to
1 newton-metre and, in terms of SI base units:
 An energy unit that is used in atomic physics, particle physics and high energy physics
is the electronvolt (eV). One EV is equivalent to 1.60217653×10−19 J. In spectroscopy the
unit cm−1 = 0.000123986 EV is used to represent energy since energy is inversely
proportional to wavelength from the equation .
 In discussions of energy production and consumption, the units barrel of oil equivalent
and ton of oil equivalent are often used.
 When discussing amounts of energy released in explosions or bolide impact events, the
TNT 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 in
rotational motion is typically expressed in newton-metres. This is not a simple
coincidence: a torque of 1 newton-metre applied on 1 radian requires exactly 1 newton-
metre = 1 joule of energy.

 The mole, the unit of amount of substance, was subsequently added to
this list and the degree Kelvin renamed the kelvin.
 There are two types of SI units, base units and derived units. Base units
are the simple measurements for time, length, mass, temperature,
amount of substance, electric current and light intensity. Derived units
are constructed from the base units, for example, the watt, i.e. the unit for
power, is defined from the base units as m2·kg·s−3. Other physical
properties may be measured in compound units, such as material density,
measured in kg·m-3.

 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 the
horsepower-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 is
often given in units of kilowatt-hours per year (kWh/yr). This is actually a measurement of
average 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 one
gram of water by 1 Celsius degree, at a pressure of 1 atm. For thermochemistry a calorie of
4.184 J is used, but other calories have also been defined, such as the International Steam
Table calorie of 4.1868 J. Food energy is measured in large calories or kilocalories, often
simply 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 the
non-SI, but convenient, units electronvolts (eV). The Hartree (the atomic unit of energy) is
commonly used in calculations. Historically Rydberg units have been used.
Other Units Of Energy

 Spectroscopy
 In spectroscopy and related fields it is common to measure energy levels in units
of reciprocal centimetres. These units (cm−1) are strictly speaking not energy
units but units proportional to energies, with hc being the proportionality
constant.
 Explosions
 A gram of TNT releases 980–1100 calories upon explosion. To define the tonne of
TNT, this was arbitrarily standardized by letting 1000 thermochemical calories =
1 gram TNT = 4184 J (exactly).
Other Units Of Energy

When calculating kinetic energy (work to accelerate a mass from zero speed to some finite
speed) relativistically - using Lorentz transformations instead of Newtonian mechanics,
Einstein discovered an unexpected by-product of these calculations to be an energy term
which does not vanish at zero speed. He called it rest mass energy - energy which every mass
must possess even when being at rest. The amount of energy is directly proportional to the
mass 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 individual
particles is destroyed, but the inertia equivalent of the system of the two particles (its
invariant mass) remains (since all energy is associated with mass), and this inertia and
invariant mass is carried off by photons which individually are massless, but as a system
retain their mass. This is a reversible process - the inverse process is called pair creation - in
which the rest mass of particles is created from energy of two (or more) annihilating
photons. In this system the matter (electrons and positrons) is destroyed and changed to
non-matter energy (the photons). However, the total system mass and energy do not
change during this interaction.
 In general relativity, the stress-energy tensor serves as the source term for the gravitational
field, in rough analogy to the way mass serves as the source term in the non-relativistic
Newtonian approximation.
 It is not uncommon to hear that energy is "equivalent" to mass. It would be more accurate
to state that every energy has an inertia and gravity equivalent, and because mass is a form
of energy, then mass too has inertia and gravity associated with it.
Relativity

 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 food
molecules, the latter mostly carbohydrates and fats, of which glucose (C6H12O6) and stearin (C57H110O6) are
convenient 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 + HPO4
2− → 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 for
other metabolism (at each stage of a metabolic pathway, some chemical energy is converted into heat). Only a
tiny 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 the
energy they receive (chemical energy or radiation), and it is true that most real machines manage higher
efficiencies. In growing organisms the energy that is converted to heat serves a vital purpose, as it allows the
organism tissue to be highly ordered with regard to the molecules it is built from. The second law of
thermodynamics 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 higher
energy efficiencies than more complex ones, but the complex organisms can occupy ecological niches that are
not available to their simpler brethren. The conversion of a portion of the chemical energy to heat at each step
in a metabolic pathway is the physical reason behind the pyramid of biomass observed in ecology: to take just
the 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

 Energy density is a term used for the amount of useful energy
stored in a given system or region of space per unit volume.
 For fuels, the energy per unit volume is sometimes a useful
parameter. In a few applications, comparing, for example, the
effectiveness of hydrogen fuel to gasoline it turns out that hydrogen
has a higher specific energy than does gasoline, but, even in liquid
form, a much lower energy density.
Energy Density

 The kinetic energy of an object is the energy which it possesses due to its motion.It is
defined as the work needed to accelerate a body of a given mass from rest to its stated
velocity. Having gained this energy during its acceleration, the body maintains this kinetic
energy unless its speed changes. The same amount of work is done by the body in
decelerating 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 can
take 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. The
same bullet is stationary from the point of view of an observer moving with the same
velocity as the bullet, and so has zero kinetic energy. By contrast, the total kinetic energy of a
system of objects cannot be reduced to zero by a suitable choice of the inertial reference
frame, unless all the objects have the same velocity. In any other case the total kinetic energy
has a non-zero minimum, as no inertial reference frame can be chosen in which all the objects
are stationary. This minimum kinetic energy contributes to the system's 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 a
speed v is ½ mv². In relativistic mechanics, this is only a good approximation when v is much
less than
 the speed of light.
Kinetic Energy

 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 exist
at one point), or a non-rotating rigid body depends on the mass of the body as well as its speed. The kinetic
energy is equal to the mass multiplied by the square of the speed, multiplied by the constant 1/2. In formula
form:
 where is the mass and is the speed (or the velocity) of the body. In SI units (used for most modern scientific
work), 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 per
second (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 hit
something and push it, doing work on what it hits. The kinetic energy of a moving object is equal to the work
required to bring it from rest to that speed, or the work the object can do while being brought to rest: Net force x
distance = 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 as
much kinetic energy. For example, a car traveling twice as fast as another requires four times as much distance
to stop, assuming a constant braking force. As a consequence of this quadrupling, it takes four times the work to
double 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 body
with 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

 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 nor
leave, does not change in whatever reference frame it is measured. Thus, the chemical energy
converted to kinetic energy by a rocket engine is divided differently between the rocket ship and
its 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., is
conserved over time, regardless of the choice of reference frame. Different observers moving
with 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 frame
that gives the minimum value of that energy is the center of momentum frame, i.e. the reference
frame in which the total momentum of the system is zero. This minimum kinetic energy
contributes to the invariant mass of the system as a whole.
Newtonian Kinetic Energy

 In physics, potential energy is the energy of a body or a system due to the
position of the body or the arrangement of the particles of the system.The SI
unit for measuring work and energy is the Joule (symbol J).
 The term "potential energy" was coined by the 19th century Scottish engineer
and physicist William Rankine,although it has links to Greek philosopher
Aristotle's concept of potentiality.
Potential Energy

 However, over large variations in distance, the approximation that g is constant is no
longer valid, and we have to use calculus and the general mathematical definition of
work to determine gravitational potential energy. For the computation of the potential
energy we can integrate the gravitational force, whose magnitude is given by
Newton's 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 and
M2 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 by
summing, 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 bodies
consist of, and applying the previous on the particle level we get the negative
gravitational binding energy. This potential energy is more strongly negative than the
total potential energy of the system of bodies as such since it also includes the
negative gravitational binding energy of each body. The potential energy of the
system of bodies as such is the negative of the energy needed to separate the bodies
from each other to infinity, while the gravitational binding energy is the energy
needed to separate all particles from each other to infinity.
 There fore ,
General Formula

 Elastic potential energy
 Calculation of elastic potential energy
 The elastic potential energy stored in a stretched spring can be calculated by
finding the work necessary to stretch the spring a distance x from its un-
stretched length:
 an ideal spring will follow Hooke's 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 mechanical
equilibrium. More involved calculations can be found at elastic potential
energy.
Kinds Of Potential Energy

 The elastic potential energy stored in a stretched spring can be
calculated by finding the work necessary to stretch the spring a
distance x from its un-stretched length:
 an ideal spring will follow Hooke's Law:
 The work done (and therefore the stored potential energy) will
then be:
Calculation OF Elastic Potential Energy

 Chemical potential energy is a form of potential energy related to
the structural arrangement of atoms or molecules. This arrangement
may be the result of chemical bonds within a molecule or otherwise.
Chemical energy of a chemical substance can be transformed to
other forms of energy by a chemical reaction. As an example, when
a fuel is burned the chemical energy is converted to heat, same is the
case with digestion of food metabolized in a biological organism.
Green plants transform solar energy to chemical energy through the
process known as photosynthesis, and electrical energy can be
converted to chemical energy through electrochemical reactions.
 The similar term chemical potential is used to indicate the potential
of a substance to undergo a change of configuration, be it in the
form of a chemical reaction, spatial transport, particle exchange with
a reservoir, etc.
Chemical potential Energy

 An object can have potential energy by virtue of its electric charge
and several forces related to their presence. There are two main
types of this kind of potential energy: electrostatic potential energy,
electro dynamic potential energy (also sometimes called magnetic
potential energy).
 Plasma formed inside a gas filled sphere
Electrical Potential Energy

 In case the electric charge of an object can be assumed to be at rest, it has
potential energy due to its position relative to other charged objects.
 The electrostatic potential energy is the energy of an electrically charged
particle (at rest) in an electric field. It is defined as the work that must be done
to move it from an infinite distance away to its present location, in the absence
of any non-electrical forces on the object. This energy is non-zero if there is
another electrically charged object nearby.
 The simplest example is the case of two point-like objects A1 and A2 with
electrical charges q1 and q2. The work W required to move A1 from an infinite
distance 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 limits
of infinity and r.
 A related quantity called electric potential (commonly denoted with a V for
voltage) is equal to the electric potential energy per unit charge.
Electro Static Potential Energy

 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 non
zero. Magnetic potential energy is the form of energy related not only to
the distance between magnetic materials, but also to the orientation, or
alignment, of those materials within the field. For example, the needle of a
compass has the lowest magnetic potential energy when it is aligned with
the north and south poles of the Earth's magnetic field. If the needle is
moved by an outside force, torque is exerted on the magnetic dipole of the
needle by the Earth's magnetic field, causing it to move back into
alignment. The magnetic potential energy of the needle is highest when it is
perpendicular to the Earth's magnetic field. Two magnets will have
potential energy in relation to each other and the distance between them,
but this also depends on their orientation. If the opposite poles are held
apart, the potential energy will be the highest when they are near the edge
of their attraction, and the lowest when they pull together. Conversely, like
poles will have the highest potential energy when forced together, and the
lowest when they spring apart.
Magnetic Potential Energy

 Nuclear potential energy is the potential energy of the particles inside an
atomic nucleus. The nuclear particles are bound together by the strong
nuclear force. Weak nuclear forces provide the potential energy for certain
kinds of radioactive decay, such as beta decay.
 Nuclear particles like protons and neutrons are not destroyed in fission and
fusion processes, but collections of them have less mass than if they were
individually free, and this mass difference is liberated as heat and radiation
in nuclear reactions (the heat and radiation have the missing mass, but it
often escapes from the system, where it is not measured). The energy from
the Sun is an example of this form of energy conversion. In the Sun, the
process of hydrogen fusion converts about 4 million tones of solar matter
per second into electromagnetic energy, which is radiated into space.
Nuclear Potential Energy

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