Diferencia de potencial (DV) y Potencial Electrico (V)

E+

-

F=qo E

F=qo E

When the test charge is moved in the field by some external agent, the workdone by the field on the charge is equal to the negative of the work done by the external agent causing the displacement.

For an infinitesimal displacement ds of a charge, the workdone by the electric field on the charge is F. ds = q0E. ds.For a finite displacement of the charge from point A to pointB, the change in potential energy of the system DU=UB-UA is:

The integration is performed along the path that q0follows as it moves from A to B. Because the force q0E isconservative, this line integral does not depend on thepath taken from A to B.

Dividing the potential energy by the test charge gives a physical quantity that dependsonly on the source charge distribution. This quantity U/q0 is called the electric potential(or simply the potential) V. Thus, the electric potential at any point in an electric fieldis:

cantidad escalar

If the test charge is moved between two

positions A and B in an electric field, the

charge–field system experiences a change

in potential energy. The potential difference

DV = VB -VA between two points A and B in

an electric field is defined as the change in

potential energy of the system when a test

charge is moved between the points

divided by the test charge qo:

Potential difference should not be confused with difference in potential energy.The potential difference between A and B depends only on the source chargedistribution (consider points A and B without the presence of the test charge),while the difference in potential energy exists only if a test charge is movedbetween the points.Electric potential is a scalar characteristic of an electric field, independent ofany charges that may be placed in the field.

Because electric potential is a measure of potential energy per unit charge, the SI unit of both electric potential and potential difference is joules per coulomb, which is defined as a volt (V):

This equation shows that potential difference also has units of electric field times distance. From this, it follows that the SI unit of electric field (N/C) can also be expressed in volts per meter:

Therefore, we caninterpret theelectric field as ameasure of therate of changewith position ofthe electric

potential.

Example: Motion of a Proton in a Uniform Electric Field

A proton is released from rest in a uniform electric field

that has a magnitude of 8x104 V/m, as shown the

figure. The proton undergoes a displacement of 0.5 m

in the direction of E.

(A) Find the change in electric potential between

points A and B.

(B) Find the change in potential energy of the proton–field system for this displacement.

EXAMPLE

Ejercicios

Potencial electrico y energia potencialdebido a cargas puntuales

DV =

To find the electric potential at a point located a

distance r from the charge, we begin with the

general expression for potential difference:

where A and B are the two arbitrary points

shown in Figure. At any point in

space, the electric field due to the point

charge is :

where is a unit vector directed from

the charge toward the point. The quantity

E. ds can be expressed as

Como es un vector unitario, entonces:

DV =

SE CONOCE COMO

EL POTENCIAL ELECTRICO CREADO POR UNA CARGA PUNTUAL q A UNA DISTANCIA r.

LA EXPRESION

p

Q1

Q2

Qn

.

.

.

r2

r1

rn

Potencial electrico debido a una distribucion discreta de carga

EJERCICIO

1.

EJERCICIOS

EJERCICIO