Electric FieldElectric field is defined as the electric force per unit charge. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge.

Click on any of the examples above for more detail.

Lorentz force law

Using Gauss' law for electric field calculation

Index

Electric field concepts

Electromagnetic force

 

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Electric Field of Point Charge

The electric field of a point charge can be obtained from Coulomb's law:

The electric field is radially outward from the point charge in all directions. The circles represent spherical equipotential surfaces.The electric field from any number of point charges can be obtained from a vector sum of the individual fields. A positive number is taken to be an outward field; the field of a negative charge is toward it.

This electric field expression can also be obtained by applying Gauss' law.

Other electric field geometries Multiple point charges

Index

Electric field

concepts

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Electric and Magnetic ConstantsIn the equations describing electric and magnetic   fields and their propagation, three constants are normally used. One is the speed of light c, and the other two are the electric permittivity of free space ε0 and themagnetic permeability of free space, μ0. The magnetic permeability of free space is taken to have the exact value

Index

Electric field

concepts

See also relative permeability

This contains the force unit N for Newton and the unit A is the Ampere, the unit of electric current.

With the magnetic permeability established, the electric permittivity takes the value given by the relationship

where the speed of light c is given by

This gives a value of free space permittivity

which in practice is often used in the form

These expressions contain the units F for Farad, the unit of capacitance, and C for Coulomb, the unit of electric charge.

In the presence of polarizable or magnetic media, the effective constants will have different values. In the case of a polarizable medium, called a dielectric, the comparison is stated as a relative permittivity or a dielectric constant. In the case of magnetic media, the relative permeability may be stated.

Physical connections to permittivity and permeability

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Physical Connections to Electric Permittivity and Magnetic

PermeabilityExpressions for the electric and magnetic   fields in free space contain the electric permittivity ε0 and magnetic permeability μ0 of free space. As indicated in the section on electric and magnetic constants, these two quantities are not independent but are related to "c", the speed of light and other electromagnetic waves.

The electric permittivity is connected to theenergy stored in an electric field. It is involved in the expression for capacitance because it affects the amount of charge which must be placed on a capacitor to achieve a certain net electric field. In the presence of a polarizable medium, it takes more charge to achieve a given net electric field and the effect of the medium is often stated in terms of a relative permittivity.

The magnetic permeability is connected to theenergy stored in a magnetic field. It is involved in the expression for inductance because in the presence of a magnetizable medium, a larger amount of energy will be stored in the magnetic field for a given current through the coil. The effect of the medium is often stated in terms of a relative permeability.

Index

Electric field c

Coulomb's LawIndex

Electromagnetic

Like charges repel, unlike charges attract.

The electric force acting on a point charge q1 as a result of the presence of a second point charge q2 is given by Coulomb's Law:

where ε0 = permittivity of space

Note that this satisfies Newton's third law because it implies that exactly the same magnitude of force acts on q2 . Coulomb's law is a vector equation and includes the fact that the force acts along the line joining the charges. Like charges repel and unlike charges attract. Coulomb's law describes a force of infinite range which obeys the inverse square law, and is of the same form as the gravity force.

For

q1 = x10^ C

q2 = x 10^ C

and r = meters,

F= x 10^ Newtons.

A negative force implies an attractive force. The force is directed along the line joining the two charges.

Electric force example

More on Coulomb's constant

force

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Electric Force Example

The electric force between charges may be calculated using Coulomb's law.

Normal household circuits in the U.S. operate on an AC voltage of about V =120 volts. Connected to such a ciruit, the electric power relationship P = IV tells us that to use power at the rate of P = 120 watts on a 120 volt circuit would require an electric current of I = 1 ampere. One ampere of current transports one Coulomb of charge per second through the conductor. So one Coulomb of charge represents the charge transported through a 120 watt lightbulb in one second.

If two one-second collections of 1 Coulomb each were concentrated at points one meter apart, the force between them could be calculated

Index

Electromagnetic force

fromCoulomb's Law. For this particular case, that calculation becomes

If two such charges could indeed be concentrated at two points a meter apart, they would move away from each other under the influence of this enormous force, even if they had to rip themselves out of solid steel to do so!

If such enormous forces would result from our hypothetical charge arrangement, then why don't we see more dramatic displays of electrical force? The general answer is that at a given point in a wire, there is never very much departure from electrical neutrality. Nature never collects a Coulomb of charge at one point. It might be instructive to examine the amount of charge in a sphere of copper of volume one cubic centimeter. Copper has one valence electron outside of closed shells in its atom, and that electron is fairly free to move about in solid copper material (that's what makes copper a good electrical conductor). The density of metallic copper is about 9 grams/cm3 and one mole of copper is 63.5 grams so the cubic centimeter of copper contains about 1/7th of a mole or about 8.5 x 1022 copper atoms. With one mobile electron per atom, and with the electron charge of 1.6 x 10-19 Coulombs, this means there are about 13,600 Coulombs of potentially mobile charge in one cm3 of copper. Suppose we remove enough of the electrons from two spheres of copper so that there is enough net positive charge on them to suspend one of them over the other. What fraction of the electron charge must we remove? The force to lift one of the spheres of copper would be its weight, 0.088 Newtons. Assuming that the net charge resides at the points of the spheres most distant from each other because of the charge repulsion, we can set the force of repulsion equal to the weight of a sphere. The radius of a one cm3 sphere is 0.62 cm, so we will treat the force as that between two point charges 2.48 cm apart (i.e., twice the sphere diameter apart). Using Coulomb's law, this requires a charge of 7.8 x 10-8 Coulombs. Compared to the total mobile charge of 13,600 Coulombs, this amounts to removing just one valence electron out of every 5.7 trillion (5.7 x 1012) from each copper sphere. The final result is that the removal of just one out of roughly six trillion of the free electrons from each copper sphere would cause enough electric repulsion on the top sphere to lift it, overcoming the gravitational pull of the entire Earth!

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Coulomb's Constant

The constant of proportionality k appearing in Coulomb's law is often called Coulomb's constant. Note that it can be expressed in terms of another constant, ε0 = permittivity of space.

When describing the electric forces in atoms and nuclei, it is often convenient to work with the product of Coulomb's constant and the square of the electron charge since that product appears in electric potential energy and electric force expressions. That product in units appropriate for atomic and nuclear processes is:

Index

Electromagnetic force

The electric force between charges may be calculated using Coulomb's law.

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Permittivity is a material property that expresses the force between two point charges in the material. Relative permittivity is the factor by which the electric field between the charges is decreased or increased relative to vacuum.]

Electric charge is the physical property of matter that causes it to experience a force when placed

in an electromagnetic field. There are two types of electric charges: positive and negative. Positively

charged substances are repelled from other positively charged substances, but attracted to

negatively charged substances; negatively charged substances are repelled from negative and

attracted to positive. An object is negatively charged if it has an excess of electrons, and is otherwise

positively charged or uncharged. The SI derived unit of electric charge is thecoulomb (C), although

in electrical engineering it is also common to use the ampere-hour (Ah), and in chemistry it is

common to use the elementary charge (e) as a unit. The symbol Q is often used to denote charge.

The early knowledge of how charged substances interact is now called classical electrodynamics,

and is still very accurate ifquantum effects do not need to be considered.

The electric charge is a fundamental conserved property of some subatomic particles, which

determines theirelectromagnetic 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 (See

also: magnetic field).

An electromagnetic field (also EMF or EM field) is a physical field produced by electrically charged

objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field

extends indefinitely throughout space and describes the electromagnetic interaction. It is one of the

four fundamental forces of nature (the others are gravitation, weak interaction and strong

interaction).

The field can be viewed as the combination of an electric field and a magnetic field. The electric field

is produced by stationary charges, and the magnetic field by moving charges (currents); these two

are often described as the sources of the field. The way in which charges and currents interact with

the electromagnetic field is described by Maxwell's equations and the Lorentz force law.

From a classical perspective in the history of electromagnetism, the electromagnetic field can be

regarded as a smooth, continuous field, propagated in a wavelike manner; whereas from the

perspective of quantum field theory, the field is seen as quantized, being composed of

individual particles.[citation needed]

In physics, the kinetic energy of an object is the energy that it possesses due to its motion.[1] It is

defined as the workneeded 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.

In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at

a speed v is  . In relativistic mechanics, this is a good approximation only when v is much less

than the speed of light.

The kinetic energy in the moving cyclist and the bicycle can be converted to other forms. For

example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to

a complete halt at the top. The kinetic energy has now largely been converted to gravitational

potential energy that can be released by freewheeling down the other side of the hill. Since the

bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling.

The energy is not destroyed; it has only been converted to another form by friction. Alternatively the

cyclist could connect a dynamo to one of the wheels and generate some electrical energy on the

descent. The bicycle would be traveling slower at the bottom of the hill than without the generator

because some of the energy has been diverted into electrical energy. Another possibility would be

for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through

friction as heat.

Like any physical quantity that is a function of velocity, the kinetic energy of an object depends on

the relationship between the object and the observer's frame of reference. Thus, the kinetic energy

of an object is not invariant.

Spacecraft use chemical energy to launch and gain considerable kinetic energy to reach orbital

velocity. In a perfectly circular orbit, this kinetic energy remains constant because there is almost no

friction in near-earth space. However it becomes apparent at re-entry when some of the kinetic

energy is converted to heat. If the orbit iselliptical or hyperbolic, then throughout the orbit kinetic

and potential energy are exchanged; kinetic energy is greatest and potential energy lowest at closest

approach to the earth or other massive body, while potential energy is greatest and kinetic energy

the lowest at maximum distance. Without loss or gain, however, the sum of the kinetic and potential

energy remains constant.

Kinetic energy can be passed from one object to another. In the game of billiards, the player

imposes kinetic energy on the cue ball by striking it with the cue stick. If the cue ball collides with

another ball, it slows down dramatically and the ball it collided with accelerates to a speed as the

kinetic energy is passed on to it. Collisions in billiards are effectively elastic collisions, in which

kinetic energy is preserved. In inelastic collisions, kinetic energy is dissipated in various forms of

energy, such as heat, sound, binding energy (breaking bound structures).

Flywheels have been developed as a method of energy storage. This illustrates that kinetic energy is

also stored in rotational motion.

Several mathematical descriptions of kinetic energy exist that describe it in the appropriate physical

situation. For objects and processes in common human experience, the formula ½mv² given

by Newtonian (classical) mechanics is suitable. However, if the speed of the object is comparable to

the speed of light, relativistic effectsbecome significant and the relativistic formula is used. If the

object is on the atomic or sub-atomic scale, quantum mechanical effects are significant and a

quantum mechanical model must be employed.

The cars of a roller coaster reach their maximum kinetic

energy when at the bottom of their path. When they start

rising, the kinetic energy begins to be converted to

gravitational potential energy. The sum of kinetic and

potential energy in the system remains constant, ignoring

losses to friction.

Common symbols KE, Ek, or T

SI unit joule (J)

Derivations from

other quantitiesEk = ½mv2

Ek = Et+Er

In physics, potential energy is the energy stored in an object due to its position in a force field or in

a system due to its configuration.[1] [2] Common types include the gravitational potential energy of an

object that depends on its vertical position and mass, the elastic potential energy of an extended

spring, and the electric potential energy of a charge in an electric field. The SI unit for energy is

the joule (symbol J).

The term potential energy was introduced by the 19th century Scottish engineer and

physicist William Rankine,[3][4] although it has links to Greek philosopher Aristotle's concept

of potentiality. Potential energy is associated with forces that act on a body in a way that depends

only on the body's position in space. These forces can be represented by a vector at every point in

space forming what is known as a vector field of forces, or a force field.

If the work of a force field acting on a body that moves from a start to an end position is determined

only by these two positions, and does not depend on the trajectory of the body, then there is a

function known as potential energy that can be evaluated at the two positions to determine this work.

Furthermore, the force field is determined by this potential energy and is described as derivable from

a potential.

n the case of a bow and arrow, when the archer does work

on the bow, drawing the string back, some of the chemical

energy of the archer's body is transformed into elastic

potential-energy in the bent limbs of the bow. When the

string is released, the force between the string and the arrow

does work on the arrow. Thus, the potential energy in the

bow limbs is transformed into the kinetic energy of the arrow

as it takes flight.

Common

symbolsPE, U, or V

SI unit joule (J)

Derivations from

other quantitiesU = m · g · h(gravitational)

U = ½ · k · x2 (elastic)

U = C · V2 / 2 (electric)

U = -m · B (magnetic)