Across the surface of a charged conductor

Options

A. field is continuous
B. potential is continuous
C. field is discontinuous
D. potential is discontinuous

Answer

To solve the question regarding the nature of the electric field and electric potential across the surface of a charged conductor, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of a Charged Conductor**:
- A conductor in electrostatic equilibrium has charges distributed on its surface. Inside the conductor, the electric field is zero.

2. **Electric Field Inside and Outside the Conductor**:
- The electric field (E) inside a charged conductor is zero (E = 0). This is because charges redistribute themselves in such a way that they cancel any internal electric fields.
- Outside the conductor, the electric field is non-zero and directed outward from the surface of the conductor.

3. **Nature of Electric Field Across the Surface**:
- The electric field is discontinuous at the surface of the conductor. This is because it abruptly goes from a non-zero value (outside) to zero (inside). Therefore, we can conclude that the electric field is discontinuous across the surface of the charged conductor.

4. **Electric Potential Inside and Outside the Conductor**:
- The electric potential (V) inside the conductor is constant because the electric field is zero (E = -dV/dr = 0 implies dV = 0). Thus, the potential does not change within the conductor.
- The electric potential is continuous across the surface of the conductor. While it may change from a higher value outside to a constant value inside, there is no abrupt jump in potential.

5. **Conclusion**:
- The electric field across the surface of a charged conductor is discontinuous.
- The electric potential across the surface of a charged conductor is continuous.

### Final Answer:
- The electric field is discontinuous, and the electric potential is continuous.