What is potential difference? derive an expression for potential difference between two points.

The potential difference two points inside the electric field is define as the amount of work done in moving a unit positive test charge from one point to another point against the electric field.


                        Suppose a unit positive charge is at any point ‘p’ so that OP=x. since the force experienced by the unit positive test charge is equal to the electric field intensity at the point.

Thus, the small work done in moving a unit positive charge from point ‘P’ to point ‘Q’ is:


Negative sign shows that unit positive charge and displacement are in opposite direction.

Therefore, total work done in moving a unit positive charge ‘B’ to point ‘A’ is:

By definition, the potential difference between two points ‘A’ and ‘B’ is:


This gives the potential difference between two points ‘A’ and ‘B’.