Which of the following statements is false for a perfect conductor ?

Options

A. The surface of the conductor is an equipotential surface.
B. The electric field just outside the surface of a conductor is perpendicular to the surface.
C. The charge carried by a conductor is always uniformaly distributed over the surface of the conductor.
D. none of these

Answer

To determine which statement is false for a perfect conductor, we need to analyze each of the given statements based on the properties of conductors in electrostatics.

### Step-by-Step Solution:

1. **Understanding the Properties of a Perfect Conductor**:
- A perfect conductor is a material that allows electric charges to move freely within it. In electrostatic equilibrium, the electric field inside a perfect conductor is zero.

2. **Evaluating the First Statement**:
- **Statement**: "The surface of the conductor is an equipotential surface."
- **Analysis**: This statement is true. Since the electric field inside a conductor is zero, there can be no potential difference across any part of the surface. Therefore, the surface of a conductor is indeed an equipotential surface.

3. **Evaluating the Second Statement**:
- **Statement**: "Electric fields just outside the surface of the conductor are perpendicular to the surface."
- **Analysis**: This statement is also true. The electric field lines must be perpendicular to the surface of a conductor in electrostatic equilibrium. If they were not, charges would continue to move until they reached a state where the field is perpendicular.

4. **Evaluating the Third Statement**:
- **Statement**: "The charge carried by a conductor is always uniformly distributed over the surface of the conductor."
- **Analysis**: This statement is false. While charges tend to distribute themselves on the surface of a conductor, the distribution can be non-uniform, especially in the presence of external electric fields or if the conductor has an irregular shape. Therefore, it is not accurate to say that the charge is always uniformly distributed.

5. **Conclusion**:
- Based on the analysis, the false statement regarding a perfect conductor is the third one: "The charge carried by a conductor is always uniformly distributed over the surface of the conductor."

### Final Answer:
The false statement is: "The charge carried by a conductor is always uniformly distributed over the surface of the conductor."

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