Summarizing Electric Potential in a Uniform Electric Field

Summary

• The voltage between points A and B is

  \(\left.\begin{array}{c}{V}_{\text{AB}}=\mathrm{Ed}\\ E=\cfrac{{V}_{\text{AB}}}{d}\end{array}\right\}\text{(uniform}\phantom{\rule{0.25em}{0ex}}E\phantom{\rule{0.25em}{0ex}}\text{- field only),}\)

  where \(d\) is the distance from A to B, or the distance between the plates.
• In equation form, the general relationship between voltage and electric field is

  \(E=\phantom{\rule{0.25em}{0ex}}–\cfrac{\Delta V}{\Delta s},\)

  where \(\Delta s\) is the distance over which the change in potential, \(\Delta V\), takes place. The minus sign tells us that \(\mathbf{\text{E}}\) points in the direction of decreasing potential.) The electric field is said to be the gradient (as in grade or slope) of the electric potential.

Glossary

scalar

physical quantity with magnitude but no direction

vector

physical quantity with both magnitude and direction