Electrical potential

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Physical size
Surname electrical potential
Size type electrical potential
Formula symbol
Size and
unit system
unit dimension
SI V M L 2 T −3 I −1
cgs g 1/2 · cm 1/2 · s -1 M 1/2 L 1/2 T −1
Gauss ( cgs ) Statvolt (statV) M 1/2 L 1/2 T −1
HLE ( cgs ) Statvolt (statV) M 1/2 L 1/2 T −1
esE ( cgs ) Statvolt (statV) M 1/2 L 1/2 T −1
emE ( cgs ) Abvolt (abV) M 1/2 L 1/2 T −1
Planck 1 M L 2 T −2 Q −1

The electric potential or electrostatic potential , also electric or electrostatic potential , (Greek small letter Phi ) is a physical quantity in classical electrodynamics .

The electrical potential is the quotient of the potential energy of a test charge and the value of this charge :

A time-invariant, i.e. H. Assuming a static electric field that assigns a potential to every point in space; one therefore speaks of a potential field . The difference between the potentials at two points is called the electrical voltage between these points (see also potential and voltage ).

A potential field can be visualized using equipotential surfaces .

In the SI system of units, the electrical potential has the unit volt ( ) or watt per ampere ( ) or joule per coulomb ( ).

Electrical potential of a point charge

The electrical potential of a point charge with a charge of different sizes. Blue is negative charge, red is positive.

The electrical potential of a point charge , also called Coulomb potential , is given by in the SI system of units

Here designated

  • the electric charge
  • the electric field constant
  • the position of the point under consideration relative to the point charge.

In the Heaviside-Lorentz system of units , due to is simplified

Electric potential of a static electric field

In the flame probe experiment , the electrical potential can be measured as a voltage.

If the electric field is known, the potential at the point with the position vector , starting from a zero potential in the position , can be calculated using a curve integral :

Usually zero potential is chosen. It follows:

Conversely, the electric field strength can be expressed by the gradient of the potential:

The Poisson's equation applies to a continuous charge distribution :


Here designated

Especially for the empty space there is . is therefore a harmonious function .

The electrical potential is constant inside a conductor .

Electric potential of a dynamic electric field

The following applies to dynamic electric fields:

The electric field can therefore not be represented as a gradient field of the electric potential. Instead, the gradient field of the potential is:

Conversely, the potential at a location can be determined using a curve integral based on a zero potential in any location chosen :

With the usual choice of as zero potential follows:

Here designated

With the Lorenz calibration , the Poisson equation follows for a continuous charge distribution :

Here designated

For stationary fields we have and , so that the formulas change back to those for static fields.

Individual evidence

  1. a b Wolfgang Demtröder: Experimentalphysik 2 Electricity and Optics . 7., corr. and exp. Edition. Springer-Verlag GmbH, Berlin 2018, ISBN 978-3-662-55789-1 .