Three identical conducting plain parallel plates, each of area A are held with equal distance between successive surfaces. Charges`Q`, `2Q`, and `3Q` are placed on them.Neglecting edge effects, find the distribution of charges on the six surfaces.

Explanation

To solve the problem of charge distribution on three identical conducting parallel plates with charges \( Q \), \( 2Q \), and \( 3Q \), we will analyze the electrostatic behavior of the system step by step.

### Step-by-Step Solution:

1. **Understanding the Setup:**
- We have three parallel plates (let's call them Plate 1, Plate 2, and Plate 3) with equal area \( A \).
- The charges on these plates are \( Q \) on Plate 1, \( 2Q \) on Plate 2, and \( 3Q \) on Plate 3.

2. **Identifying Surfaces:**
- Each plate has two surfaces. Thus, we have six surfaces in total:
- Surface 1 (Plate 1, front)
- Surface 2 (Plate 1, back)
- Surface 3 (Plate 2, front)
- Surface 4 (Plate 2, back)
- Surface 5 (Plate 3, front)
- Surface 6 (Plate 3, back)

3. **Charge Distribution:**
- Since the plates are conductors, charges will redistribute themselves due to electrostatic repulsion until electrostatic equilibrium is reached.

4. **Analyzing the Charges:**
- **Plate 1** has a charge of \( Q \). This charge will distribute itself evenly on its surfaces:
- Surface 1 (front) will have \( +Q \).
- Surface 2 (back) will induce a charge of \( -Q \) on Plate 2's front surface due to electrostatic induction.

- **Plate 2** has a charge of \( 2Q \). The back surface (Surface 4) will also have a charge of \( -Q \) from Plate 1's influence:
- Surface 3 (front) will have \( +2Q \) (original charge) + \( -Q \) (induced charge) = \( +Q \).
- Surface 4 (back) will have \( -Q \).

- **Plate 3** has a charge of \( 3Q \). The back surface (Surface 6) will have a charge of \( +3Q \):
- Surface 5 (front) will have \( +3Q \) (original charge) + \( -Q \) (induced charge from Plate 2) = \( +2Q \).

5. **Final Charge Distribution:**
- Surface 1 (Plate 1, front): \( +Q \)
- Surface 2 (Plate 1, back): \( -Q \)
- Surface 3 (Plate 2, front): \( +Q \)
- Surface 4 (Plate 2, back): \( -Q \)
- Surface 5 (Plate 3, front): \( +2Q \)
- Surface 6 (Plate 3, back): \( +3Q \)

### Summary of Charge Distribution:
- Surface 1: \( +Q \)
- Surface 2: \( -Q \)
- Surface 3: \( +Q \)
- Surface 4: \( -Q \)
- Surface 5: \( +2Q \)
- Surface 6: \( +3Q \)