Across the surface of a charged conductor, the electric

Options

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

Answer

To solve the question regarding the behavior of electric fields and potentials across the surface of a charged conductor, we can follow these steps:

### Step 1: Understand the behavior of electric fields in conductors
In electrostatic equilibrium, the electric field inside a conductor is zero. This is because any excess charge resides on the surface of the conductor, and the charges rearrange themselves in such a way that they cancel any internal electric fields.

**Hint:** Remember that in electrostatic conditions, charges in a conductor will always move until they reach a state where the electric field inside is zero.

### Step 2: Analyze the electric field at the surface of the conductor
At the surface of a charged conductor, the electric field is not continuous. There is a sudden change in the electric field from zero inside the conductor to a non-zero value just outside the surface. This indicates that the electric field is discontinuous across the surface.

**Hint:** Consider what happens to the electric field as you move from inside the conductor to just outside it. What does this imply about continuity?

### Step 3: Understand the behavior of electric potential in conductors
The electric potential throughout the entire volume of a conductor in electrostatic equilibrium is constant. This means that there is no difference in potential anywhere inside the conductor. However, there is a potential difference between the inside and outside of the conductor.

**Hint:** Think about how potential relates to electric field. If the electric field is zero inside, what does that say about the potential?

### Step 4: Conclusion
Based on the analysis:
- The electric field is discontinuous at the surface of a charged conductor (it jumps from zero inside to a non-zero value outside).
- The electric potential is continuous across the surface of the conductor (it remains constant inside and changes smoothly outside).

Thus, the correct options are:
- Electric field is discontinuous (Option 3).
- Electric potential is continuous (Option 2).

**Final Answer:** The correct options are 2 (potential is continuous) and 3 (field is discontinuous).