Question

Suppose you have a map of equipotential surfaces spaced 1.0 V apart. Which of the following statements about the electric field is correct (select all that apply)?

A) The electric field has the magnitude 1.0 V/m at each point on each of the equipotential surfaces
B) The electric field is tangent to both of the equipotential surfaces
C) At each point on each of the equipotential surfaces, the electric field points in a direction that is orthogonal to the equipotential surface
D) The electric field is stronger wherever the equipotential surfaces are spatially closer together

Answer 1

The electric field is perpendicular to equipotential surfaces and is stronger where these surfaces are closer together, but we cannot assume the field strength without knowing the spatial separation between the surfaces.

Step-by-step explanation:

When analyzing a map of equipotential surfaces with a spacing of 1.0 V apart, certain characteristics of the electric field can be deduced. First, option (A) is incorrect because the value of 1.0 V/m as the magnitude of the electric field can only be assumed if the surfaces are spaced 1.0 m apart, which is not provided in this scenario. Option (B) is incorrect since the electric field is not tangent but rather perpendicular to the equipotential surfaces. Counter to (B), (C) is correct stating that at each point on an equipotential surface, the electric field is indeed directed in a way that is orthogonal (perpendicular) to the surface. Lastly, (D) is correct because the electric field is stronger where equipotential surfaces are closer together, indicating a greater change in potential over a shorter distance.