Electric potential

 Potential 

Potential in general

Potential is a scalar quantity expressing the ability of a certain physical field to act on material points, or charges located in it.

The value of the potential is relative, it refers to a certain place with a chosen zero potential (e.g. for an electric field, the ground is usually chosen as the zero potential, for a gravitational field, the zero potential is at infinity, for thermodynamic potentials in the equilibrium state of the system).

Conservative physical field

A conservative field is a physical field { E(x, y, z) }of vector character of a certain force for which there is a scalar function – potential – satisfying the relation. (A scalar product, is a position vector determining a given location in space) Conversely, the magnitude of the intensity of a physical field can be determined using the gradient of the potential:. A conservative physical field can therefore be characterized at each of its points by a scalar potential, which has a certain numerical value at each point. Thanks to the introduction of the potential, the vector field can be described by a scalar quantity.

The electric field of a point charge:, and represent individual equipotential levels, the red dot is a point on a certain equipotential level. The green arrow shows the potential gradient vector at point, the blue arrow of the opposite direction the electric field intensity vector. Both vectors, like the electric field line, are perpendicular to the equipotential line.

Potential energy Potential, or positional energy, is the energy that every body has in a potential field of a certain force.

The change in potential energy is defined as, where and are the potential energies belonging to the original and resulting positions in the potential field. If this change occurred along the direction of the potential gradient, the potential energy decreased and, according to the law of conservation of energy, work was done by the system. If the position changed against the direction of the gradient, the potential energy increased and an external energy force of magnitude had to be supplied to the system.

The magnitude of the change in potential energy does not depend on the way the system got from the initial state to the final state, only on the value of the initial and resulting potential energy. It follows that the value of the resulting change in potential energy during a circular event is zero.

Potential energy, like potential, is relative and refers to some chosen point with zero potential energy. It can therefore also take on positive and negative values.

Types of potentials

Depending on the type of potential field, we distinguish several types of potentials.

Electric potential

Electric potential is a scalar quantity describing the potential energy of a unit charge in a constant conservative electric field. It is defined as the amount of energy required to transfer a charge from a given point to a point of zero potential. The surface of the Earth is usually chosen as the point of zero potential.

Electric potential is denoted by, its unit is.

The value of the electric potential can be calculated:

, where the work required to transfer the charge is.

In the field of a point charge for the potential, the relation applies, where the constant depends on the permittivity of the medium, the size of the charge causing the electric field and the distance from it.

The differential rise in electric potential can be calculated as.

The electric field intensity is the negative gradient of the electric potential.

From a biophysical point of view, the electric potential is of fundamental importance as a component of the electrochemical potential of protons in the respiratory chain, or as a component of the resting membrane potential and the action potential.

Scalar magnetic potential

A static magnetic field, i.e. a field created by a non-moving permanent magnet or a conductor with a constant current, can be called a potential field and assigned a scalar potential. Its unit is. Its size can be calculated:

In the case of a constant current conductor, where is the current flowing through the conductor and is the solid angle at which the conductor is seen from a given point.

In the case of a permanent magnet, the magnetic potential is calculated as, where is the magnetic moment vector, is the position vector of a point in the magnetic field, and is the distance from the dipole.

The differential rise in magnetic potential can be calculated as.

The intensity of the magnetic field is the negative gradient of the scalar magnetic potential, respectively, where represents the permeability of the medium.

A variable magnetic field is not conservative and is therefore described by a vector potentia l.

Gravitational potential

Gravitational potential is a scalar quantity describing the potential energy of a body of unit mass in the gravitational field of other bodies. Since the range of the gravitational force is infinite, the point of zero potential is chosen at infinity, and therefore the value of the gravitational potential is negative.

Gravitational potential is denoted by, its unit is , respectively. The size can be calculated:

In the gravitational field of a mass point or a spherical body, the relation, where is the gravitational constant, is the mass of the body and the distance from it.

In a homogeneous gravitational field by the relation, where the magnitude of the gravitational field intensity vector (corresponds to the gravitational acceleration at a given location)

The differential rise in gravitational potential can be calculated as

The gravitational field intensity is the negative gradient of the gravitational potential

Thermodynamic potentials

are quantities with an energy dimension used mainly in thermodynamic and chemical calculations to establish the conditions of dynamic equilibrium of reactions. Individual potentials differ from each other in their natural variables, therefore each is suitable for calculations during reactions taking place in different conditions.

The name thermodynamic potentials is used as an analogy to the potentials of force fields, as they can be used to determine important quantities (state quantities, heat capacities,...) of given systems. They also have formally the same properties as potential energy.


 * It depends only on the location (space).
 * There is their complete differential.
 * The size of their change does not depend on the method, only on the initial and final state.
 * In a circular event, their change is zero.
 * In the equilibrium state, they reach their minimum.
 * Used thermodynamic potentials:


 * Internal energy,
 * enthalpy,
 * Gibbs free energy,
 * Helmholtz free energy.