24.5 : Finding Electric Potential From Electric Field

For a system of charges, it is easy to calculate the system's potential because potential is a scalar quantity. However, in some instances where calculating the electric field is more straightforward than finding the potential, the electric field is used to calculate the system's potential. For a positive charge, the electric field is radially outward, and the potential is positive at any finite distance from the positive charge. In such an electric field, the motion away from the positive charge along the direction of the electric field lowers the value of the electric potential. However, if the movement is toward the positive charge, opposite to the direction of the electric field, then the electric potential increases. Alternatively, for an electric field of a negative charge, movement away from the negative charge increases the electric potential.

The energy per electron is very small in macroscopic situations, a tiny fraction of a joule, but, on a submicroscopic scale, such energy per particle (electron, proton, or ion) can be of great importance. For example, even a tiny fraction of a joule can be significant enough for these particles to destroy organic molecules and harm living tissue. The particle may do its damage by direct collision, or it may create harmful X-rays, which can also inflict damage. It is helpful to have an energy unit related to submicroscopic effects.

An electron accelerated through a potential difference of 1 V is given energy of 1 eV. It follows that an electron accelerated through 50 V gains 50 eV. A potential difference of 100,000 V (100 kV) gives an electron energy of 100,000 eV (100 keV), and so on. Similarly, an ion with a double positive charge accelerated through 100 V gains 200 eV of energy. These simple relationships between accelerating voltage and particle charges make the electron volt a simple and convenient energy unit in such circumstances. The electron volt is commonly employed in submicroscopic processes—chemical valence energies and molecular and nuclear binding energies are among the quantities often expressed in electron volts. Nuclear decay energies are on the order of 1 MeV (1,000,000 eV) per event and can, thus, produce significant biological damage.