How to Calculate Equipotential

In physics, equipotential is defined as a collection of points over which a field potential does not change. In a two dimensional coordinate system, equipotentials are represented by lines; in three dimensions, equipotentials are surfaces. Equipotential is typically introduced as a concept in electrostatics, but it also applies to other topics in physical sciences such as gravity and radiation. Knowledge of the location(s) of equipotential surface(s) serves as an aid for visualizing electric field lines. The surface of a source that gives rise to a force field is itself an equipotential.

Things You'll Need

  • Problem Text
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Instructions

  1. Problem Steps

    • 1

      Draw a diagram of the problem by drawing the geometry of the source(s) and the electric field lines emanating from the source(s). Electric field lines are represented by vectors that point in directions of decreasing potential.

    • 2

      Write the equation for the electric field if it is given in the problem statement. If it is not given, derive it from the information given about the source(s). For a source q that produces electric field E, the source-to-electric field relationship takes the form of E = kq/(r^2), where k is a constant and r is the distance at which the observation point sits from the source. Your electric field equation will look similar to this; it may carry an extra factor that indicates the geometry of the problem, but the units never change.

    • 3

      Divide the electric field by its own magnitude to get the normal unit vector to the equipotential surface. Use this quantity along with the point of interest to find the tangent plane to that surface. The tangent plane is the equation for the equipotential surface.

    • 4

      Check that your answer is correct by taking the dot product of the electric field with a vector that satisfies the equation of the tangent plane. Since the electric field is perpendicular to the equipotential surface, the dot product should equal zero. If the problem is conceptual, explain how the equipotential surfaces would be generally represented (perpendicular to the given electric field). This will give you the equation for the surface, not the value of the potential.

    • 5

      Plug the point of interest into the potential function to find the value of the potential. If the function is not given, integrate the electric field over the proper coordinates using the point of interest as the upper bound and the origin of the problem as the lower bound to get that equipotential value.

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