Equipotential Surfaces for a Uniform Electric Field in the Z-Direction

Concept

Equipotential surfaces are surfaces where the electric potential remains constant. In a uniform electric field, equipotential surfaces are always perpendicular to the field lines.

Given Condition

• The electric field is uniform and directed along the Z-axis.
• In a uniform field, the potential difference between two points is given by: V=−Ez⋅zV = – E_z \cdot z which means the potential only changes along the Z-direction.

Equipotential Surface Characteristics

• The equipotential surfaces must be planes parallel to the X-Y plane (i.e., perpendicular to the Z-axis).
• Each plane represents a constant potential VV, and different planes correspond to different potential values.

Diagram Explanation

• The Z-axis represents the direction of the electric field.
• The X-Y planes at different heights (Z = constant) represent different equipotential surfaces.
• Since the electric field is uniform, these surfaces are equally spaced.

Drawing

To visualize, draw:

1. A set of horizontal planes (parallel to the X-Y plane) at different Z values.
2. Label each plane with a different potential V1,V2,V3V_1, V_2, V_3, etc., decreasing or increasing along the Z-direction.
3. Indicate the uniform electric field (E) as vertical arrows along the Z-axis.