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# Difference between electric potential and potential difference

”  Electric potential at a point in an electric field is equal to the amount of  work  done in bringing a unit positive charge from infinity to that point.”If  W  is the work done in moving a unit positive charge from infinity to a certain point in the field ,the electric potential V at this point would be given by:

V=W/q

It implies that electric potential is measured relative to some reference point and like potential energy can be measured only the change in potential between two points.It is a scalar quantity,its SI unit is volt which is equal to JC¯1. volt:”If one joule of work is done against the electric field in bringing one coulomb positive charge from infinity to a point in the electric field then the potential at that point will be one volt.”or “one joule of work done on a charge of one coulomb is equal to one volt”.

## How to find electric potential?

Let us consider a positive charge q which is allowed to move in an electric field produced between two oppositely charged parallel plates as shown in figure. The positive charge will move from plate B to A and will gain K.E .If it is to be moved from A to B,an external force is needed to make the charge move against the electric field and will gain P.E .Let us impose a condition that as the charge is moved from A to B, it is moved keeping electrostatic equilibrium,i.e.,it moves with uniform velocity.This condition could be achieved by applying a force F equal and opposite to qE at every point along its path as shown in figure. The work done by the external force against the electric field increases electrical potential energy of the charge that is moved. Let WAB be the work done by the force in carrying the positive charge qo from A to B while keeping the charge in equilibrium.The change in its potential energy is given by ΔU= WAB or

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UB and UA =  WAB

Where  UA and Uare defined to be the potential energies at points A and B,respectively. To describe electric field we introduce the idea of electric potential difference.The  potential difference between two points A and B in an electric field is defined as “The work done in carrying a unit positive charge from points A to B while keeping the charge in equilibrium ,that is ,

ΔV=VB-VA=WAB/q=ΔU/q

Where VA and VB are defined electric potentials at points A and B  respectively.Electric potential energy difference and electric potential difference between the points A and B  are related as

ΔU=q0ΔV=WAB

Thus the potential difference between the two points can be defined as “the difference of the potential energy per unit charge.” Unit of potential difference is volt

1volt=1joule/1coulomb

That is,a potential difference of 1 volt exists between two points if work done in moving a unit positive charge from one point to other ,keeping equilibrium,is one joule. In order to give a concept of electric potential at a point in an electric field,we must have a reference to which we assign zero electric potential.this point is usually taken at infinity .Thus in equation

ΔV=VB-VA=WAB/q

we take A to be at infinity and choose Va=0,the electric potential  at B will be

VB=WB/q

or dropping the subscripts we have an equation

V=W/q

which states that the electric potential at any point in an electric field is equal to work done in bringing  a unit positively charge from infinity to that point keeping it in equilibrium.It is to be noted that potential at a point is still potential difference between the potential  at that point and potential at infinity.Both potential and potential differences are scalar quantities  because both W and q0 are scalars. Watch video about electric potential and potential difference to clear your concepts visually.

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Video about Difference between electric potential and potential difference:

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