Electric Potential Difference

Electric potential, denoted by V (or occasionally φ), is a scalar physical quantity that describes the potential energy of a unit electric charge in an electrostatic field. It is defined as the amount of work energy needed to move a unit of electric charge from a reference point to a specific point in an electric field. If a positive test charge q in an electric field has electric potential energy U_a at some point a (relative to some zero potential energy), electric potential V_a at this point is:

V_a = U_a/q

In the International System of Units (SI), electric potential is expressed in units of joules per coulomb (J⋅C⁻¹) , or volts (V). Although the concept of electric potential is useful in understanding electrical phenomena, only differences in potential energy are measurable. These differences in potential energy are measured with a voltmeter.

Although the concept of electric potential is useful in understanding electrical phenomena, only differences in potential energy are measurable. For electric circuits, electric potential difference is known as voltage. It is the difference in electric potential between two points of electrical circuit.

The electric potential can be generalized to electrodynamics, so that differences in electric potential between points are well-defined even in the presence of time-varying fields. In this general case, the potential difference between two points a and b  is given by the line integral of vector E. The potential at a given point can be found by first finding E and then carrying out this integral.

These differences in potential energy are measured with a voltmeter. The potential difference between two points equals the amount of work that would be required to move a unit positive test charge between those points.  When the electric force does positive work on a charge, the kinetic energy increases and the potential energy decreases. The difference in potential energy, U_b — U_a, is equal to the negative of the work, W_ba, done by the electric field as the charge moves from a to b; so the potential difference V_ba is:

Note that an electric potential difference is analogous to a gravitational potential difference. In the latter case, a force is exerted on objects with mass. Charges experience a force when there is an electric potential difference. The direction of the force depends on the sign of the charge. The electric field E is analogous to g, which we called the acceleration due to gravity but which is really the gravitational field. Everything we learned about gravity, and how masses respond to gravitational forces, can help us understand how electric charges respond to electric forces.