electric field

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electric field

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electric field

Definition/Summary

An electric field is a vector field that permeates the space around an electrical charge. The electric field of a charge is what mediates the force between that charge and any other charge in the vicinity. The electric field can be obtained by using Coulomb's Law, or Gauss's Law, or by finding the negative of the gradient of the electrical potential in the space surrounding the charge.

Electric field, normally denoted by the letter

Click to see the LaTeX code for this image

, has units of volts per metre (or newtons per coulomb), and dimensions of mass.length/charge.time².

It is derived from a (non-unique) vector and scalar potential,

and

(and the magnetic field

is derived from the same vector potential).

Equations

(1)

(2)

Potential equations:

(3)

The two source-free Maxwell equations (Faraday's Law and Gauss' Law for Magnetism) follow immediately by differentiating the potential equations:

(4)

Energy density:

(5)

Total energy:

(6)

Scientists

Michael Faraday(1791-1867)
James Clerk Maxwell(1831-1879)

Recent forum threads on electric field

Breakdown

Physics
> Electromagnetism
>> Mathematical Methods

Images

Extended explanation

The electric field, along with the magnetic field, were originally conceived by Michael Faraday to explain the long range nature of those forces. The mathematical development of this field theory was left to Maxwell.

Since the electric field can accelerate charged bodies, it must be able to store electrical potential energy. The energy density of an electrical field is given by equation (5). In order to find the total energy stored in the field, the density function must be integrated over all space, thus giving rise to equation (6).

Time-varying electric fields are somewhat more difficult to find due to the fact that they can be created by time-varying magnetic fields as well as a time-varying potential. This phenomenon, known as Electromagnetic Induction, is represented in the derivative of the magnetic vector potential in equation (4).

After some manipulation of (4), you will obtain Faraday's Law, a much more well known representation of induction:

Reason for definition of electric field:

Electric field

is defined so that multiplying it by the charge

of a body gives the force

on that body:

This is the electric part of the Lorentz force:

So it must have dimensions of force/charge, or work/charge.length, and so can be measured in newtons/coulomb.

Since work (or energy) can be measured in electron-volts, work/charge can be measured in volts, and so electric field can also be measured in volts/metre.

By comparison, magnetic field is defined so that multiplying it by the charge of a body and cross-producting it with the velocity of the body gives the force on that body:

Similarly, therefore, magnetic field must have dimensions of force/charge.velocity, and can be measured in volts/metre per metre/second, or volt.seconds/metre², which are webers/metre², or teslas.

Commentary

tiny-tim @ 03:27 PM Aug27-09

wikipeida is remarkably comprehensive, but not entirely reliable. The PF library does have selective links to particularly good wikipedia articles. Since wikipedia is fairly easy to search, is there any point in linking to run-of-the-mill articles, or worse?

nirax @ 07:29 AM Aug27-09

it would be a nice idea to provide a link to Wikipedia article on any such concepts illustrated in this forum.

nshtkmar1977 @ 02:18 AM May6-09

we often say that electric field at a space is the force exerted on a charge when its magnitude is very small? we know that a charge can not exert force on itself, so why putting this condition that test charge tends to zero?

GKM @ 07:08 AM Feb25-09

how does the electric field pattern looks like when a charged particle moves with uniform relativistic velocity?

freehuman79 @ 07:29 PM Jan30-09

is there any thing about the conservation of angular momentum in electric field?
~EDIT(tiny-tim): angular momentum is only conserved in a magnetic field.

Robtai @ 03:41 AM Jan19-09

http://en.wikipedia.org/wiki/Electric_field

tiny-tim @ 09:08 AM Oct12-08

Added vector and scalar potential to Definition, and made associated changes to Equations.

tiny-tim @ 05:12 AM Jul7-08

Added dimensions, units, links to scientists, and

pzlded @ 11:49 AM May13-08

The electric field surrounding a point charge extends to infinity and is not limited by an insulator or a conductor. The energy a point charge gains approaching another point charge is lost at some point during departure.

The range of a voltage field differs from the range of a point charge field. A voltage field is limited to the component (resistor or capacitor) that holds the voltage field.

For example, The definition of electron-volt is the energy a point charge gains while passing through a voltage gradient.

In a synchrotron, a voltage field incrementally adds a fixed amount of electron volts to point charges each time the point charges pass through the voltage field. A constant magnetic field applies centripetal force that keeps the point charges in a circular path (w/o adding kinetic energy to the point charges).

Collections of point charges cannot add the incremental accelerations, because point charge approach energy can be lost during departure.

G01 @ 11:28 PM Apr29-08

OK. I think I fixed the errors you pointed out, olgranpappy. How does it look now?

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