In physics, the **electrical potential** is a scalar field: it has a magnitude, but no direction, at every point in space. It determines (for a given system at a given point) the ratio of potential energy to
electric charges at that point. The electric field is the negative gradient of the electrical potential.

The electrical potential is therefore measured in units of energy per unit of electric charge:

Electrical potential is (mathematically) analogous to temperature: every point in space has a given temperature, and temperature gradients (analogous to the electric field) determine the direction of heat flows.

Classical mechanics explores the concepts such as force, energy, potential etc. in more detail.

There is a direct relationship between force and potential energy. As an object moves in the direction the force accelerates it, its potential energy decreases. For example, the gravitational potential energy of a cannonball at the top of a tower is greater than at the base of the tower. As the object falls, that potential energy decreases and is translated to motion, or inertial energy.

For certain forces, it is possible to define the "potential" of a field such that the potential energy of an object due to a field is dependent only on the position of the object with respect to the field. Those forces must affect objects depending only on the intrinsic properties of the object and the position of the object, and obey certain other mathematical rules.

Two such forces are the gravitational force (gravity) and the electric force. The potential of an electric field is called the electrical potential.

The electrical potential can also be calculated using the electric field **E**, thus:

If **E** is constant, then φ_{E} looks like this:

The electrical potential created by a point charge q can be shown to have the following form:

The electrical potentials due to a system of point charges may be computed as the sum of the respective potentials, which simplifies calculations significantly since adding scalar fields is very much easier than adding the electrical fields, which are vector fields.

See also potential difference.

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