A conductor with a cavity is charged positively and its surface charge density is `sigma`. If E and V represent the electric field and potential, then inside the cavity

Options

A. E = 0 and V = 0
B. E = 0 and `sigma`- constant
C. V = 0 and `sigma` = constant
D. E = 0 and V = constant

Answer

To solve the problem regarding the electric field (E) and potential (V) inside a cavity of a positively charged conductor with surface charge density σ, we can follow these steps:

### Step 1: Understand the properties of conductors
In electrostatics, the electric field inside a conductor in electrostatic equilibrium is zero. This is due to the fact that charges redistribute themselves on the surface of the conductor until the electric field within the conductor cancels out.

**Hint:** Remember that in electrostatic equilibrium, the electric field inside a conductor is always zero.

### Step 2: Analyze the cavity inside the conductor
Since the conductor has a cavity, we need to consider the implications of having a cavity within a conductor. The charges on the surface of the conductor will redistribute themselves in such a way that the electric field inside the cavity is also zero. This is because any electric field would cause charges to move, contradicting the condition of electrostatic equilibrium.

**Hint:** Think about how charges behave in response to electric fields and how they distribute themselves on the surface of conductors.

### Step 3: Determine the electric field (E) inside the cavity
Since the electric field inside the cavity is zero, we can conclude:
\[ E = 0 \]

**Hint:** Recall that if the electric field is zero, it means that there are no forces acting on any test charge placed inside the cavity.

### Step 4: Determine the electric potential (V) inside the cavity
The electric potential inside the cavity will be constant. This is because the electric field is zero, and thus there is no change in potential within the cavity. The potential inside the cavity will be equal to the potential at the surface of the conductor.

**Hint:** Remember that the potential difference is related to the electric field; if the electric field is zero, the potential does not change.

### Step 5: Conclusion
From the analysis, we can summarize:
- The electric field inside the cavity is zero: \( E = 0 \)
- The electric potential inside the cavity is constant: \( V = V_0 \) (where \( V_0 \) is the potential at the surface of the conductor).

Thus, the correct answer is that inside the cavity, the electric field is zero, and the potential is constant.

**Final Answer:**
- \( E = 0 \)
- \( V = \text{constant} \)