Which of the following is NOT the property of equipotential surface?

Options

A. They do not cross each other.
B. The rate of change of potential with distance on them is zero.
C. For a uniform electric field they are concentric spheres.
D. They can be imaginary spheres.

Answer

To determine which of the following is NOT a property of equipotential surfaces, let's analyze the properties of equipotential surfaces step by step.

### Step-by-Step Solution:

1. **Definition of Equipotential Surface**: An equipotential surface is a surface on which the electric potential is the same at every point. This means that if you move along the surface, the potential does not change.

2. **Properties of Equipotential Surfaces**:
- **Do Not Cross Each Other**: Equipotential surfaces cannot intersect. If they did, it would imply that at the point of intersection, there are two different potentials, which is not possible.
- **Rate of Change of Potential is Zero**: On an equipotential surface, the electric potential does not change, hence the rate of change of potential with distance is zero.
- **Concentric Spheres in Uniform Electric Fields**: In a uniform electric field, equipotential surfaces are not necessarily concentric spheres. Instead, they are planes perpendicular to the direction of the electric field.
- **Imaginary Surfaces**: Equipotential surfaces can indeed be imaginary. They do not have to correspond to physical surfaces; they can exist in theoretical constructs.

3. **Analyzing the Options**:
- **Option 1**: They do not cross each other. (True property)
- **Option 2**: The rate of change of potential with distance on them is zero. (True property)
- **Option 3**: They are concentric spheres in a uniform electric field. (NOT a true property)
- **Option 4**: They can be imaginary surfaces. (True property)

4. **Conclusion**: The statement that is NOT a property of equipotential surfaces is that they are concentric spheres in a uniform electric field. Therefore, the answer is **Option 3**.