Electrical potential
Physical size  

Surname  electrical potential  
Size type  electrical potential  
Formula symbol  

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 timeinvariant, 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 , 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 HeavisideLorentz system of units , due to is simplified
Electric potential of a static electric field
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
 the Laplace operator
 the charge density
 the electric field constant .
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
 the Laplace operator
 the charge density
 the electric field constant
 the speed of light .
For stationary fields we have and , so that the formulas change back to those for static fields.
Individual evidence
 ↑ ^{a } ^{b} Wolfgang Demtröder: Experimentalphysik 2 Electricity and Optics . 7., corr. and exp. Edition. SpringerVerlag GmbH, Berlin 2018, ISBN 9783662557891 .