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 uniformly distributed over the surface of conductor
D. none of these

Answer

To determine which statement is false for a perfect conductor, we need to analyze the properties of perfect conductors and the options provided.

### Step-by-Step Solution:

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

2. **Analyzing the Statements**:
- Let's examine each statement one by one to find out which one is false.

3. **Statement 1**: "The surface of the conductor is an equipotential surface."
- This statement is **true**. In electrostatic equilibrium, the electric potential is constant throughout the surface of a conductor, making it an equipotential surface.

4. **Statement 2**: "Electric field just outside the surface of the conductor is perpendicular to the surface."
- This statement is **true**. The electric field lines are always perpendicular to the surface of a conductor in electrostatic equilibrium.

5. **Statement 3**: "Charge carried by a conductor is always uniformly distributed over the surface of the conductor."
- 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 irregular shapes.

6. **Conclusion**:
- The false statement among the options is **Statement 3**: "Charge carried by a conductor is always uniformly distributed over the surface of the conductor."

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