# Potential difference

When we introduce a charge into an electric field , this charge will suffer from the action of an electric force , and as a consequence, it will then gain an amount of electric potential energy , which we know as electrostatic potential . An electric field has the ability to create an area where each of the points it has has the property of conferring potential energy to any other charge that is located in its internal part. From this energy production, a totally different scalar magnitude is established which is typical of electric fields , which we know as electric potential , which will represent the electrostatic potential energy that has a unit of positive charge when it is located at the point.

## What is the potential difference?

The potential difference is the ability of the charged body to perform work by supply of electrons or its removal . It is work that is stored in the body as an electrical potential for the body to carry out work by exerting an attractive or repulsive force on charged particles.

• Definition of potential difference
• Calculation of the potential difference
• Symbol
• Unit
• Relationship with the electric field
• Importance of the potential difference
• Examples

## Definition of potential difference

The potential difference is the impulse that a certain electrical charge needs to be able to flow properly through the conductor in an electrical circuit , a current that will stop when the two points equal their electrical potential . It is also used to represent the work that a force must do to move a charge against the electric field , this from a reference point to a point where the potential can be measured . It is also known by the name of electrical voltage, and in this case, instead of taking a reference point, two points should be taken within an electric field.

## Calculation of the potential difference

Mathematically, we can calculate and express the potential difference by means of the following formula:

UA – UB 0 W / Q

The potential difference must be measured using volts , therefore, we say that an electric field has a potential difference of 1 volt when we use 1 joule to move a charge of 1 coulomb. From this statement we deduce that:

If the charge Q is positive and UA> UB , this indicates that the work that is done by the forces in the field is positive , the charge will have to move from point A to point B spontaneously . But if UA <UB is negative, it means that to move a load from A to B must perform a force in against of the field.

If the charge is negative, the previous statement works in reverse .

When two potentials UA and UB are equal, no work should be done.

## Symbol

The symbol used to define the potential difference is a V, which at the same time indicates the word volt .

## Unit

The unit used to determine the potential difference belongs to the International System unit and is the volt .

## Relationship with the electric field

It is important to know that the electric charge of a certain region has the ability to modify the space giving rise to an electric field , so an electric field can be considered as a region in which the properties have been modified by existing in the place an electrical charge. The electric field and the potential of a region in a given location can be represented dome functions position and these quantities are related reason, from the electric field can get from the electric potential , the electric field .

## Importance of the potential difference

The importance of the potential difference lies in its use within the different electrical works , which is consumed and used to carry out work that includes the use of electricity . It is used in the case of electric cookers and motors , to be able to mobilize the different gears that a machine has, just as it is important for the use of the different electrical circuits since it reflects the amount of energy that the load units have when they pass through a certain point.

## Examples

An example of a potential difference would be the following:

An electron that has a mass of m = 9.1 · 10 -31 Kg and charge q = -1.6 · 10 -19 C crosses a uniform electric field with an initial velocity of 3 · 106 m / s following the same direction and sense of said field. When traveling 4 cm his speed has been halved. Decide:

• What is the potential difference between the entry point and the point where its speed has halved.
• The potential at 4 cm if the potential at the initial point is 60 V.
• The value of the electric field intensity.

#### Data

• m = 9.110-31 Kg
• q = -1.6 10-19 C
• xA = 0 m
• xB = 4 cm = 0.04 m
• vA = 3 106 m / s
• vB = 3 · 106 m / s / 2 = 1.5 · 106 m / s