Electrical potential
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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 , 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
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. Springer-Verlag GmbH, Berlin 2018, ISBN 978-3-662-55789-1 .