Electrostatic Potential

Definition:

The electrostatic potential in an electric field at any point is defined as the work done to bring a test charge q₀ from infinity to the point per unit test charge :

) = W(

) / q₀

Notice that V() depends only on the position . The test charge gets divided out in the same way that we divided out the test charge to determine the electric field from the force.

Definition:

Electrostatic potential difference

V_AB = V_B - V_A = DU_AB/ q₀

Units:

From the above definition

[ V ] = [ W ] / [q] = J / C

In honor of Alessandro Volta (1745-1827) the unit for the electrostatic potential received the name Volt (V). Thus, by definition:

1V = 1 J / 1 C

Recall that the unit of Electric field is N / C. From the last equation, 1/ C = V / J . Combining,

N / C = V / m,

or in words: a Newton per Coulomb is the same as a Volt per meter.

Notice that (unit of charge) · (unit of potential difference) is the unit of energy. A unit very commonly used in physics is the electron Volt or eV. It is defined as follows:

Definition:

One electron-Volt is the energy an electron gains from a potential difference of 1 Volt.

1 eV = (1.6 $\cdot$ 10^-19C) $\cdot$ (1 V) = 1.6$\cdot$ 10^-19 J

The electron volt is a very small unit by our everyday standards, but its size is just right for expressing the typical energies of atomic physics. In the appendix, we have provided a JavaScript conversion engine to provide easier conversions between the different energy units.

Zero of Potential:

The logical choice, in correspondence with the zero of potential energy, is at infinity.

For practical purposes, however, infinity is a little too far, and often inaccessible. For practical purposes, the Earth is taken as the zero of potential. This is possible because the earth is such a huge conductor, that giving or taking away even large amounts of charge makes no significant change to its electric condition - its potential remains substantially unchanged. In fact, the Earth has a certain fixed (it so happens, negative) potential with respect to infinity. And potential (like potential energy) is always defined up to an additive constant.