Electrostatics

Electrostatics is a branch of physics that studies slow-moving or stationary electric charges.

Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing.

Electrostatic phenomena arise from the forces that electric charges exert on each other.

There are many examples of electrostatic phenomena, from those as simple as the attraction of plastic wrap to one's hand after it is removed from a package, to the apparently spontaneous explosion of grain silos, the damage of electronic components during manufacturing, and photocopier and laser printer operation.

The electrostatic model accurately predicts electrical phenomena in "classical" cases where the velocities are low and the system is macroscopic so no quantum effects are involved.

It also plays a role in quantum mechanics, where additional terms also need to be included.

Coulomb's law states that:[5] The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.The force is along the straight line joining them.

, in units of Newtons per Coulomb or volts per meter, is a vector field that can be defined everywhere, except at the location of point charges (where it diverges to infinity).

(called source points) generates the electric field at

The fact that the force (and hence the field) can be calculated by summing over all the contributions due to individual source particles is an example of the superposition principle.

and can be obtained by converting this sum into a triple integral: Gauss's law[9][10] states that "the total electric flux through any closed surface in free space of any shape drawn in an electric field is proportional to the total electric charge enclosed by the surface."

Many numerical problems can be solved by considering a Gaussian surface around a body.

Mathematically, Gauss's law takes the form of an integral equation: where

The divergence theorem allows Gauss's Law to be written in differential form: where

The definition of electrostatic potential, combined with the differential form of Gauss's law (above), provides a relationship between the potential Φ and the charge density ρ: This relationship is a form of Poisson's equation.

[11] In the absence of unpaired electric charge, the equation becomes Laplace's equation: If the electric field in a system can be assumed to result from static charges, that is, a system that exhibits no significant time-varying magnetic fields, the system is justifiably analyzed using only the principles of electrostatics.

[12] The validity of the electrostatic approximation rests on the assumption that the electric field is irrotational, or nearly so: From Faraday's law, this assumption implies the absence or near-absence of time-varying magnetic fields: In other words, electrostatics does not require the absence of magnetic fields or electric currents.

In some problems, both electrostatics and magnetostatics may be required for accurate predictions, but the coupling between the two can still be ignored.

Electrostatics and magnetostatics can both be seen as non-relativistic Galilean limits for electromagnetism.

[13] In addition, conventional electrostatics ignore quantum effects which have to be added for a complete description.

, points from regions of high electric potential to regions of low electric potential, expressed mathematically as The gradient theorem can be used to establish that the electrostatic potential is the amount of work per unit charge required to move a charge from point

with the following line integral: From these equations, we see that the electric potential is constant in any region for which the electric field vanishes (such as occurs inside a conducting object).

We integrate from a point at infinity, and assume a collection of

The total electric potential energy due a collection of N charges is calculating by assembling these particles one at a time: where the following sum from, j = 1 to N, excludes i = j: This electric potential,

: This second expression for electrostatic energy uses the fact that the electric field is the negative gradient of the electric potential, as well as vector calculus identities in a way that resembles integration by parts.

; they yield equal values for the total electrostatic energy only if both are integrated over all space.

On a conductor, a surface charge will experience a force in the presence of an electric field.

This force is the average of the discontinuous electric field at the surface charge.

This average in terms of the field just outside the surface amounts to: This pressure tends to draw the conductor into the field, regardless of the sign of the surface charge.

Learning materials related to Electrostatics at Wikiversity

A tabby cat covered in packing peanuts.
Foam peanuts clinging to a cat's fur due to static electricity . The cat's fur becomes charged due to the triboelectric effect . The electric field of the charged fur causes polarization of the molecules of the foam due to electrostatic induction , resulting in a slight attraction of the light plastic pieces to the fur. [ 1 ] [ 2 ] [ 3 ] [ 4 ] This effect is also the cause of static cling in clothes.
The electrostatic field (lines with arrows) of a nearby positive charge (+) causes the mobile charges in conductive objects to separate due to electrostatic induction . Negative charges (blue) are attracted and move to the surface of the object facing the external charge. Positive charges (red) are repelled and move to the surface facing away. These induced surface charges are exactly the right size and shape so their opposing electric field cancels the electric field of the external charge throughout the interior of the metal. Therefore, the electrostatic field everywhere inside a conductive object is zero, and the electrostatic potential is constant.
Summary of electrostatic relations between electric potential, electric field and charge density. Here, .