An arrangement of three large metallic parallel plates with respective charges marked in figure is shown . What is the charge appearing on the left face of plate B ?

Options

A. Zero
B. `(Q_(2) - Q_(1))/( 2)`
C. `-Q_(1)`
D. `+ Q_(2)`

Answer

To find the charge appearing on the left face of plate B in the arrangement of three large metallic parallel plates, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Plates and Their Charges**:
- We have three plates: A, B, and C.
- Let the charge on plate A be \( Q_1 \), the charge on plate B be \( 0 \) (since it is uncharged), and the charge on plate C be \( Q_2 \).

2. **Understand the Charge Distribution**:
- The charge on a metallic plate redistributes itself in response to the electric fields created by the other plates.
- Since plate B is neutral, it will have induced charges on its faces due to the presence of plates A and C.

3. **Determine the Charge on the Left Face of Plate B**:
- The charge on the left face of plate B will be influenced by the charge on plate A.
- The electric field created by plate A will induce a charge on the left face of plate B.

4. **Use the Concept of Induced Charge**:
- The induced charge on the left face of plate B can be calculated using the principle of superposition.
- The total charge on the left face of plate B can be found using the formula:
\[ Q_{\text{left face of B}} = \frac{Q_1 - Q_2}{2} \]
- This formula comes from the fact that the charge distribution will balance out due to the influence of the other plates.

5. **Final Calculation**:
- Therefore, the charge appearing on the left face of plate B is:
\[ Q_{\text{left face of B}} = \frac{Q_1 - Q_2}{2} \]

### Conclusion:
The charge appearing on the left face of plate B is \( \frac{Q_1 - Q_2}{2} \).