From the following statements for an equipotential surface, the incorrect statement is

Options

A. The potential difference between two points on the surface is zero
B. The direction of electric intensity is perpendicular to the surface at every point
C. No work is done in moving an electric charge on the surface.
D. The shape of the surface is always sperical

Answer

To determine the incorrect statement regarding equipotential surfaces, let's analyze each statement step by step:

### Step-by-Step Solution:

1. **Understanding Equipotential Surfaces**:
- An equipotential surface is defined as a surface where the electric potential is constant throughout. This means that if you take any two points on this surface, the potential difference between them is zero.
- **Statement 1**: "The potential difference between two points on the surface is zero."
- This statement is **correct** because, by definition, all points on an equipotential surface have the same potential.

2. **Electric Field Direction**:
- The electric field direction is always perpendicular to the equipotential surface.
- **Statement 2**: "The direction of electric intensity is perpendicular to the surface at every point."
- This statement is **correct**. The electric field lines are always perpendicular to equipotential surfaces.

3. **Work Done in Moving a Charge**:
- When moving a charge along an equipotential surface, no work is done because the potential difference is zero.
- **Statement 3**: "No work is done in the moving of charge."
- This statement is **correct**. Since the potential difference is zero, the work done is also zero.

4. **Shape of the Equipotential Surface**:
- The shape of an equipotential surface is not necessarily spherical; it depends on the charge distribution.
- **Statement 4**: "The shape of the surface is always spherical."
- This statement is **incorrect**. Equipotential surfaces can take various shapes depending on the configuration of the electric field. For example, around a dipole, the equipotential surfaces are not spherical.

### Conclusion:
The incorrect statement regarding equipotential surfaces is **Statement 4**: "The shape of the surface is always spherical."

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