Question

In a uniform electric field, equipotential surfaces must be:
This question has multiple correct options
A. be plane surfaces
B. be normal to the direction of the field
C. be spaced such that surfaces having equal differences are separated by equal distances
D. have decreasing potentials in the direction of the field

Answer 1

A uniform electric field is such that it is directed towards the same direction at all points of the space. The equipotential surfaces are those which have the same potential due to an electric field on every point on the surface.

Complete step by step answer:
Following diagram shows a uniform electric field.

Therefore, a uniform electric field is such that it is directed towards the same direction at all points of the space in a uniform manner.
The equipotential surfaces can be defined as the two-dimensional surfaces in an electric field on which electric potential is the same at all points of the surface. For a uniform electric field, the equipotential surfaces look like follows:

The uniformity of electric field leads to a planar equipotential surface which is perpendicular to the direction of the field.
The electric field is related to the electric potential by the following relation:
$\overrightarrow E = - \overrightarrow \nabla V$
This negative sign implies that the electric decreases with increase in electric field. As the direction of electric field is direction in which the electric field increases, therefore, the equipotential surfaces possess decreasing potential in the direction of electric field.
As we know that the electric potential is given as
$V = \dfrac{1}{{4\pi { \in _0}}}\dfrac{q}{r}$
This relation implies that there is a linear relationship between electric potential and distance r. This means that the equipotential surfaces must be spaced such that surfaces having equal differences are separated by equal distances.

Based on above discussion, we can say that all the options given to us are correct.

Note:
1. It should be noted that two equipotential surfaces shall not intersect each other whether we have uniform or non-uniform electric fields.
2. We can also use the electric field due to a stationary charge as an example of a uniform electric field. In that case, the equipotential surfaces are in the shape of concentric circles but all the properties discussed in this question hold there as well.