9.2.B—Describe the relationship between electric potential and electric field

Describe the relationship between electric potential and electric field.

• The value of an electric field component in any direction at a given location is equal to the negative of the spatial rate of change in electric potential at that location. Relevant equation: =− EdV dx x
• The change in electric potential between two points can be determined by integrating the dot product of the electric field and the displacement along the path connecting the points. Relevant equation:
• Electric field vector maps and equipotential lines are tools to describe the field produced by a charge or configuration of charges and can be used to predict the motion of charged objects in the field.
  • i. Equipotential lines represent lines of equal electric potential. These lines are also referred to as isolines of electric potential. 44 Electric Potential UNIT 9
  • ii. Isolines are perpendicular to electric field vectors. An isoline map of electric potential can be constructed from an electric field vector map, and an electric field map may be constructed from an isoline map.
  • iii. An electric field vector points in the direction of decreasing potential.
  • iv. There is no component of an electric field along an isoline.