Electric Potential

Electric potential When a charged particle moves in an electric field, the field exerts a force that can do work on the particle. This work is expressed in terms of electric potential energy. This potential energy depends on the position of the charged particle in the electric field. Moving a positive test charge against the direction direction of an electric field requires work by an external force. This work would in turn increase the potential energy of the object. On the other hand, the movement of a positive test charge in the direction of an electric field would be without the need of work by an external force. This motion would result in the loss of potential energy. Potential energy is the stored energy energy of position of an object Consider the electric field due to a positively charged Sphere. Sphere. The direction of the electric field is in the direction that a positive test charge would be pushed; in this case, the direction is outward away from the sphere. Work would be required to move a positive test charge towards the sphere against the electric field. The amount of force involved in doing the work is dependent upon the amount of charge being moved (according to Coulomb's law of electric force). The greater the charge on the test charge, the greater the repulsive force and the more work that would have to be done on it to move it the same distance. If two objects of different charge - with one being twice the charge of the other - are moved the same distance into the electric field, then the object with twice the charge would require twice the force and thus twice the amount of  work. This work would change the potential energy by an amount that is equal to the amount of work done. Thus, the electric potential energy is dependent upon the amount of charge on the object experiencing experiencing the field and upon the location within the field. Electric potential energy is dependent dependent upon two types of quantities: 1) Electric charge - and

2) Distance from source - the location within the electric field Electric potential Electric potential is the potential energy per charge. Electric Potential =

  

So the electric potential V at any point in an electric field is given as: V = That gives

 

, where U is the potential energy and q is the test charge.

U =



( 1)

Potential energy and charge both are scalars, so electrical potential is a scalar. Electrical potential is also defined as: The work required to transfer a unit positive electric charge from an infinite distance to a given point against an electric field. The SI unit of Electrical potential is Volt. If the work required transferring one coulomb charge from an infinite distance against the field is 1 Joule, the potential would be 1 volt. 1 volt = 1 joule / coulomb Calculating Electric Potential

The force 1on a test charge q moving in the electric field by a single stationary point charg is given as F =





 

Work done by this force on charge q is given as W  

V V

=

Fr 

= = =



Er 

(2) 





   

(3)



Units of Potential Difference is Volt (V) 1 Volt = 1 Joule/Coulomb

Potential Due to Collection of Point Charges Potetial due to collection of point charges is r1 V

=

 



 

 Where  denotes the sum of   for different charges located at different places.

Equipotential surfaces: An equipotential surface is a surface on which the potential has the same value at every point. At a point where a field line crosses an equipotential surface, the two are perpendicular. When all charges are at rest, the surface of a conductor is an equipotential surface. And all points in the interior of a conductor are at the same potential.

Equipotential lines are always perpendicular to the electric field. Movement along an equipotential surface requires no work because such movement is always perpendicular to the electric field.

Potential difference The potential difference between the two points is the amount of work that would be required to move a unit positive test charge between those points. When a particle with charge q moves from a point a, where the potential is Va to a point b of potential Vb , the change in the potential energy U is (4)

Ua - Ub = q ( Va – Vb ) = q Vab, Vab is called the potential difference between a and b Electron Volts If q = e = 1.602 x 10

-19

C

Vab = 1Volt then change in energy is Ua - Ub = 1.602 x 10

-19

C x 1 V = 1.602 x 10

-19

J=1eV