Electric field

The electric field is a physical box that operates by the Coulomb force of electric charges. The electric field is a ubiquitous phenomenon that explains the propagation of light and radio waves, the transmission of electric energy and the operation of electronic circuits. It also causes the binding of the electron to the nucleus and thus takes a great influence on the shape of the material.

The electric field is described by the vector field of the electric field, which assigns to each point in space for a vector direction and magnitude of the electric field strength.

Electric fields caused by the electric charges, or by temporal changes in magnetic fields. The properties of the electric field will be described along with the characteristics of the magnetic field in Maxwell's equations.

• 5.1 Electric field of a line charge
• 5.2 Electric field of a surface charge
• 5.3 Homogeneous electric field ( plate capacitor )
• 5.4 Electric field of a dipole

General

Description as a vector field

The electric field can be described by the vector field of the electric field strength. Of the electric field strength, the electric flux density depends.

• The vector field of the electric field assigns to each point in space to the space-and time -dependent vector of the electric field strength. The electric field strength describes the force acting on charges and can be determined experimentally by this force effect. It works at a location on an electrical test charge in the absence of magnetic field strength, the electric field strength is defined by

• The vector field of the electric flux density assigns to each point in space to the space-and time -dependent vector of the electric flux density. Measurement technology can only be done indirectly, the electric flux density. Two characteristics of the electric flux density are used:

The energy density of the electric field resulting from the electric field intensity and the electric flux density by the equation

The relationship between the electric field intensity and the electric flux density is dependent on the medium and is not linear due to the electrical polarization in general. Since the electric polarization in a material with a charge transfer, and consequently, connected to a power transmission, the polarization is not instantaneous, and thereby also frequency dependent. For many media, you can still approximate a linear relationship in the form

Assume the electric field constant and the permittivity.

In a vacuum, with the relationship between the two fields is strictly linear, and we have:.

Link to the magnetic field

The electric field in a general manner, both spatially and time dependent. It is linked by Maxwell's equations and special relativity closely with the magnetic field. In the special theory of relativity its vector components are therefore grouped together inseparably with those of the magnetic field to a tensor. Depending in which reference to an observer is located, i.e., in which the relative movement to any existing space charges will be transformed via the Lorentz transform the electric field in a magnetic field and vice versa.

Differences in electrostatics and electrodynamics

In electrostatics only charges at rest are considered. Without currents, there is no magnetic field, the electrostatic field is therefore not only stationary, ie invariant in time, but also irrotational, so it has a potential.

In electrodynamics one must also consider electric fields, which are caused by time-varying magnetic fields (electromagnetic induction). A particularly important example, the electromagnetic waves such as light, which consist of electric and magnetic fields concatenated. Due to the close relationship between electric and magnetic field holds you both together in electrodynamics for electromagnetic field.

Near power rather than action at a distance

Up to detect electromagnetic waves by Heinrich Hertz was the question of whether the forces that exert the charges to each other, directly in terms of action at a distance or come about through the agency of the space in terms of a proximity effect.

• The prototype of an action at a distance theory associated Coulomb law is the law. In line with the ideas of an action at a distance theory, the essential elements of the array when Coulomb's law are given by the charges and occur both in the equations for the force, as well as in the equations for the energy ( in addition to the required information on the geometry).

• In a theory of contiguous action, however, exist only between such greats relationships that exist at the same time in the same place. An example of a theory of contiguous action are the Maxwell 's equations. According to the ideas of Maxwell's equations, the most important of which to the fields in the electrical phenomena. The electrical energy is not considered as the loads and adherent conductors, but is located in the insulators and vacuum and can be transported through them.

As long as only slow changes in the electrical and magnetic quantities are considered, it is not crucial from a physical point of view out if you linked to the physical phenomena one or the other idea. However, considering that momentum and energy can propagate in space by means of electromagnetic waves, so can be difficult to bring in line with the observations of the idea of ​​action at a distance.

In summary, it goes from today's perspective, assuming that the interaction is mediated between the charges of a field, and speaks of the electric field. Since the force depends on the electric field at that point, but not directly by the electric field at other points, it is a proximity effect. If the position of one of the charges associated with the electric field, so the change of the field propagates at the speed of light in the room. A relativistic view of the electric field leads to the so-called electromagnetic field. This can both impulse and energy to record, and has as energy and momentum carrier the same reality, such as a particle.

Quantize the electric field

In the context of quantum mechanics, the fields are still considered to be classic, even if the states of the interacting particles are usually quantized. Quantum field theories combine principles of classical field theories (for example, electrodynamics ), and describe particles and fields uniform. There are not only observable (ie observable quantities ) such as energy or momentum is quantized, but also the interacting ( particle ) fields themselves; the fields are therefore treated similarly to observables. The quantization of the fields are also called second quantization.

Field line pictures

An electric field can be caused by both electric charge and the time change of the magnetic field. An intuitive representation of electric fields is obtained by field line images. These consist of oriented ( arrowed ) field lines. The following applies:

• Starting the field lines of an electric field generated by charges and ends at the loads. Such a field is called the Source field.
• Changes in the magnetic flux passing through a surface produce an electric vortex field. In this, all the electrical field lines closed in itself.

The direction of the tangent at a point on a line field indicates the direction of the field strength vector. The density ( the transverse distance ) of the flux lines is proportional to the magnitude of the field strength at that point.

Electric field of a point charge

Very easy to determine the electric field of a point charge. According to the Coulomb law is obtained for the field strength at a given point:

In this case, Q is the charge in the field-generating origin of the coordinate system of the position vector of the given point, for the associated unit vector, and constant for the electric field of the relative permittivity.

Electric field of a charge distribution

If the electric field produced by multiple point charges at the positions we obtain the field strength vector of the total field at the position according to the superposition principle by adding the individual field strength vectors:

If there is a continuous, given by the spatial charge density charge distribution, so shall apply:

Other examples of electric fields

Electric field of a line charge

The electric field of a line charge ( an infinitely long, charged wire ) with the linear charge density is given by

In this case, the base vector is directed radially from the charge line to the reference point.

Electric field of a surface charge

A surface charge ( a uniformly charged, infinitely extended thin plate ) is generated on each side a homogeneous electric field. Of the field strength vector is directed to any point perpendicular to the plate and with a positive charge from the plate, wherein a negative charge to the plate. Substituting the surface charge density required, the electric field strength is the amount

Homogeneous electric field ( plate capacitor )

The electric field between two (strictly infinite ) plane-parallel capacitor plates containing the charges of the same magnitude, but different signs, is approximately homogeneous. For the magnitude of the field strength applies:

Here, the distance between the plates, the surface of a capacitor plate, the voltage between the two plates and the amount of charge on a plate. The potential varies linearly from one plate to the other by the amount. , The plates are moved apart, the field strength remains constant, the voltage rises. The work done against the electrostatic attraction work goes into the energy of the field. Outside the capacitor, the field strength is ( ideally) equal to 0

The charges on the capacitor plates are spread over evenly to the facing plate surfaces. The absolute values ​​of the surface charge density

And the electric flux density match. However, a scalar quantity, whereas a vector.

The capacitor is not connected to an external source of charge, the value of the surface charge density does not change when a dielectric is inserted or removed between the capacitor plates. The electric field strength but changes by adding a factor in the removal.

Electric field of a dipole

An electric dipole, that is an arrangement of two point charges, and at a distance which generates a rotationally symmetrical field. For the field strength components parallel and perpendicular to the dipole axis applies to a great distance in the direction θ:

In this case, θ = 0 is on the center in the direction of the positive charge.

Exactly the formula is valid in the limit of vanishing at constant magnitude of the dipole moment.

Conductor in an electric field

Bring slowly to a conductor in a temporally constant external field, it causes the head of a charge transfer ( induction ). The interior remains free of space charges, while adjusting to the surface of a charge distribution, which keeps the inside of the head straight field-free in the sum. Outside the field lines are always perpendicular and everywhere on the conductor surface, otherwise the transverse component would cause a further charge shift. At peak results in high field strengths.