Electric Potential and Potential Difference

Consider a static electric field produced by a positive point charge. If a positive test charge moves in it, the work done on the charge is a negative change in electric potential energy.

Dividing the above work equation by the total charge on a test charge, gives the electrical potential difference.

The electric potential difference equals the amount of work done to move a unit charge from the initial to the final point.

Electric potential is the electric potential energy per unit charge. It is a scalar quantity with the SI unit of volts (joules per coulomb). 

In electronic circuits, a potential difference between two points is called voltage, which is measured by a voltmeter.

The expression for potential due to a single point charge can be generalized to a collection of point charges by taking the algebraic sum of the potential due to the individual charges.

In the case of a continuous charge distribution, the potential is calculated using the integral of charge elements over the distance where the electric potential is calculated.