Electrostatics

Electrostatics is the branch of physics that deals with static electric charges, charge distributions and the electric fields of charged bodies.

The phenomena of electrostatics stir of the forces here, the electric charges exert on each other. These forces are described by Coulomb's law. A classic example is that of grated amber attracts particles (see story). Even if the forces appear small, the electric force is, for example, compared to the gravitational force extraordinarily strong. Thus the electric force between an electron and a proton (both together form a hydrogen atom) by about 40 orders of magnitude greater than their mutual attraction, due to the gravitational force.

The electrostatics is a special case of electrodynamics for still electrical charges and static (non- time-varying ) electric fields. The electrostatics finds its analogue in the magnetostatics, which deals with stationary ( time-invariant ) currents and magnetic fields.

History

Even in ancient times it was known that certain materials such as amber, after rubbing with a cloth or fur, small light particles attract (see static electricity ). William Gilbert continued the work of Petrus Peregrinus from the 13th century and found out that other substances can be electrified by friction and developed the versorium, an early design of an electroscope. He introduced in his 1600 published book De magnets, Magnetisque Corporibus, et de Magno magnets Tellure ( German about: On the Magnet, Magnetic body and the large magnet earth) to the Neo-Latin borrowed term " electrica " for the phenomena, which he in connection with the Bernstein discovered " electron " comes from the Greek word for amber.

Survey

The force exerted by a given charge Q on an object is proportional to the charge q of the object. They can thus be represented by the equation F = q · describe E; E is the field strength of the electric field accompanying the charge Q.

From an external electric field, different effects are caused in electrical conductors and insulators. The free electric charges in conductors, such as the conduction electrons of the metals move macroscopically of such that the electric field throughout the interior of the conductor disappears (see Faraday cage). This phenomenon is called induction. On the other hand, respond to the locally bound charges in an insulator, so the electrons and nuclei of atoms, through a mutual shift, whereby the insulator is polarized.

That of an electrostatic field E of a sample Q induced force field F is conservative, that is, the potential energy E of the sample in the electrostatic field is dependent only on the position x of the sample, but not by the way in which the sample to x has been moved. This also means that the electrostatic field can be represented as the gradient of φ of electrostatic potential. The potential energy of a sample in the potential is therefore W = q · φ. The difference between two electric potentials corresponding to the electrical potential. The disappearance of the electric field E = 0 is equivalent to a constant electric potential, φ = const.

The field and thus the potential of any charge distribution in a homogeneous insulator can be easily calculated from the derived from Coulomb's law laws. ( The field in a conductor disappears. ) Such a calculation is in spatial arrangements of conductors, insulators and charges only in a few cases simple.

The electric field

For the special case of stationary electrostatic fields ( ) and vanishing electrical currents () follows from the Coulomb's law and the definition of the electric field for a point charge Q is excited by electric field at the location of the place

The electric field is a directional vector field. For a positive charge, it is just off the charge, directed for a negative charge to the charge back, which is equivalent to the repulsion of like and the attraction of opposite charges. His strength is proportional to the magnitude of the charge Q, and inversely proportional to the square of the distance from Q. The proportionality factor k ( see dielectric constant ) is the universal constant in the SI unit system and in the Gaussian system of units.

Is the measure of the electric field in SI units

Run by an amount of charges, Qi, excited field is the sum of the partial contributions ( superposition principle )

Or in the case of a continuous space charge distribution ρ, the integral

Gauss's law that describes the flow of the electric field by a closed surface area A is proportional to the strength of the surface enclosed by the charge Q

The Gaussian integral theorem associated flow and divergence of an arbitrary vector field:

From which it follows that the divergence of the electric field is proportional to the charge density:

Conservative electric field can be described by the gradient of a scalar φ electric potential

From which follows Poisson's equation:

Potential and voltage

Since an electric charge in the electric field experiences a force, is performed in its movement by the electric field work, or it must be done work in order to move the load to the electric field. From the Maxwell equations (more precisely the law of induction ) follows with that electrostatic fields are irrotational. In the conservative field, the energy needed depends only on the starting point and destination, not the exact way. " Vortex -free" means that the rotation of a field is zero (on a simply connected domain ):

Thus, a potential energy of the charge can be defined. Since the force is proportional to the charge, this also applies to the potential energy. Therefore, If the potential energy as a product of the load and a potential which is derived from the electric field directions.

The potential difference between two points is referred to as electrical voltage. The product of the charge of a particle and the voltage between two points provides the energy that is needed to bring the particles from one point to another. The unit of electric potential and the electric voltage is volts. According to the definition of potential and voltage volts applies = Joules / Coulomb.

The potential is calculated as follows:

The limits of integration arising from the choice of the zero levels. Often this is arbitrarily defined at an infinite distance. A point charge, which is located at the location which causes the potential at the site:

In the case of a continuous distribution of the space charge, the electric potential is given by the following integral:

Is it not possible to find an analytical solution of the integral, so you can develop into a power series, see multipole or Legendre polynomial # generating function.

The concept of the voltage reaches its limits when dynamic processes occur. For varying magnetic fields can still define an induced voltage, but this is no longer a potential difference defined. The energy from one point to another needed for a motion of the charge is only as long as is equal to the potential difference between the points, as the acceleration is negligible, since, according to the electrodynamics of accelerated charges emit electromagnetic waves, which must also be taken into account in the energy balance.

The energy of the electrical field

In a plate capacitor is an approximately homogeneous field. If the charge of one plate and the other plate accordingly, and is the size of a plate surface, so the field results in magnitude to

Is the constant distance between the plates, and brings to an infinitesimally small charge from the one to the other plate, so must the infinitesimal work against the electric field with the amount

Be done. The conservation of energy for this work must lead to an increase in the energy of the capacitor. However, this can only stuck in the electric field. Due to the charge transfer, the field strength increases by amount-

Solving for and substituting into the work results

But it is precisely the volume of the plate capacitor in which there is a complete E-field ( in the ideal plate capacitor can be shown that the E- field outside the plate capacitor vanishes, ie there is ). Integration takes and dividing by yields the energy density

Wherein the dielectric shift.

Occurrence, production, application

Occurrence of static charges in everyday life:

• Storm clouds, alpha emitters, beta emitters
• Electric field of the Earth ( measured for example with a flame probe )
• ESD ( electro -static discharge ): electrostatic discharge, eg after charging by running carpeted floors, use of plastic railings, sitting on chairs with synthetic fiber cover, combing with plastic comb, pulling out a synthetic fiber sweater

• Electrostatic generator
• Van de Graaff generator
• Influence

Measurement of static charges:

• Electrometer

Applications:

• Electrostatic precipitator
• Electrostatically assisted spray painting
• Fixing of sheets of paper on flatbed plotters or XY recorders