# Electric potential and electric potential difference

let us today discuss the the concept of electric potential and electric potential difference.

**Electric Potential**

Electric Potential at a point in an electric field is defined as amount of the work done in moving a unit positive test charge from infinity to that point against the electric force of the field.

Here Infinity means that the test charge is placed outside the range of electric field.

If W is the work done in bringing a positive charge q_{0} from infinity to a point in an electric field,then the potential V at that point is given by

V=W/q_{0}

If W is in joules q_{0} in coulombs.then the potential difference V is in volts.

1 volt=1 joule/1 coulomb

**Second Definition:- **Electric potential at a point,B in the electric field is defined as the negative of line integral of electric field intensity from ∞ to that point.

Thus V_{B}= -∫E.dL

**Electric potential Difference:-**

Electric Potential Difference between the two points is defined as the amount of the work done in moving a unit positive test charge from one point to the other.

The potential difference between two points ,A and B,is defined as

V_{B}-V_{A}=W_{AB}/q_{0}

Where W_{AB} is the work done by an external agent in moving a positive test charge q_{0 }from A to B.

**Second Definition:-**Electric Potential Difference between two points B and A in an electric field is the negative of the line integral of electric field intensity over a path from A to B.

**Thus **V_{B}-V_{A}= -∫E.dl