9.2 Electric Potential

Describe the electric potential due to a configuration of charged objects.

• Electric potential describes the electric potential energy per unit charge at a point in space.
• Expressions for the electric potential of charge distributions can be found using integration and the principle of superposition. Relevant equation:
  • i. The electric potential for single point charge is
  • ii. The electric potential due to multiple point charges can be determined by the principle of scalar superposition of the electric potential due to each of the point charges. Relevant equation:
• The electric potential difference between two points is the change in electric potential energy per unit charge when a test charge is moved between the two points. Relevant equation:
• Electric potential difference may also result from chemical processes that cause positive and negative charges to separate, such as in a battery. BOUNDARY STATEMENT AP Physics C: Electricity & Magnetism only expects students to use calculus to find the electric potential resulting from the following charge distributions and locations: an infinitely long, uniformly charged wire or cylinder at a distance from its central axis, a thin ring of charge at a location along the axis of the ring, a semicircular arc or part of a semicircular arc at its center, and a finite wire or line charge at a point collinear with the line charge or at a location along its perpendicular bisector.

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.