A parallel-plate capacitor is connected to a battery. A metal sheet of negligible thickness is placed between the plates. The sheet remains parallel to the plates of the capacitor.

Options

A. The battery will supply more charge.
B. The capacitance will increase.
C. The potential difference between the plates will increase.
D. Equal and opposite charges will appear on the two faces of the metal plate.

Answer

To solve the problem regarding the effect of inserting a metal sheet between the plates of a parallel-plate capacitor connected to a battery, we can follow these steps:

### Step 1: Understand the Configuration
We have a parallel-plate capacitor connected to a battery. The capacitor has two plates separated by a distance \(d\). A metal sheet of negligible thickness is inserted between the plates, remaining parallel to them.

**Hint:** Visualize the capacitor and the metal sheet to understand how they interact.

### Step 2: Analyze the Effect of the Metal Sheet
When a metal sheet is placed between the plates of the capacitor, it will affect the electric field and the charge distribution. The metal sheet will induce charges on its surfaces due to the electric field between the capacitor plates.

**Hint:** Remember that conductors in an electric field will always have charges induced on their surfaces.

### Step 3: Charge Induction on the Metal Sheet
The metal sheet will have equal and opposite charges induced on its two faces. The face of the metal sheet that is closer to the positive plate of the capacitor will acquire a negative charge, while the face closer to the negative plate will acquire a positive charge.

**Hint:** Think about how charges redistribute themselves in response to an electric field.

### Step 4: Effect on Capacitance
The introduction of the metal sheet does not change the potential difference across the capacitor plates because the battery maintains a constant voltage. The capacitance \(C\) of a capacitor is given by the formula:
\[ C = \frac{Q}{V} \]
Since the potential difference \(V\) remains constant and the charge \(Q\) does not change, the capacitance \(C\) also remains unchanged.

**Hint:** Recall that capacitance depends on the physical configuration and the dielectric properties of the materials between the plates.

### Step 5: Effect on Charge
Since the battery is connected, it will maintain the same potential difference across the capacitor. Therefore, the total charge \(Q\) on the capacitor remains constant. The presence of the metal sheet does not allow the capacitor to store more charge.

**Hint:** Consider how the battery regulates the charge on the capacitor.

### Step 6: Conclusion
Based on the analysis:
- The capacitance does not increase.
- The potential difference does not change.
- The charge does not increase.
- Equal and opposite charges appear on the two faces of the metal sheet.

Thus, the correct conclusion is that equal and opposite charges will appear on the two faces of the metal sheet.

**Final Answer:** Equal and opposite charges will appear on the two faces of the metal sheet.