In the above question, if the sheets were thick and conducting , value of E in the space between the two sheets would be

Options

A. `2sigma //in_(0)`
B. `sigma //in_(0)`
C. zero
D. `4sigma //in_(0)`

Answer

To determine the electric field \( E \) in the space between two thick conducting sheets, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two thick conducting sheets placed parallel to each other. Let's denote the charge density on the positive sheet as \( +\sigma \) and on the negative sheet as \( -\sigma \).

2. **Electric Field Due to a Single Sheet**:
- The electric field \( E \) due to an infinite sheet of charge with surface charge density \( \sigma \) is given by the formula:
\[ E = \frac{\sigma}{2\epsilon_0} \]
- This electric field points away from the sheet if the charge is positive and towards the sheet if the charge is negative.

3. **Calculating the Electric Field Between the Sheets**:
- For the positive sheet with charge density \( +\sigma \):
- The electric field in the region between the sheets (towards the negative sheet) is:
\[ E_1 = \frac{\sigma}{2\epsilon_0} \]
- For the negative sheet with charge density \( -\sigma \):
- The electric field in the same region (towards the negative sheet) is:
\[ E_2 = \frac{\sigma}{2\epsilon_0} \]
- Since both electric fields are in the same direction (towards the negative sheet), we can add them together.

4. **Net Electric Field Calculation**:
- The total electric field \( E \) in the space between the two sheets is:
\[ E = E_1 + E_2 = \frac{\sigma}{2\epsilon_0} + \frac{\sigma}{2\epsilon_0} = \frac{2\sigma}{2\epsilon_0} = \frac{\sigma}{\epsilon_0} \]

5. **Conclusion**:
- Therefore, the value of the electric field \( E \) in the space between the two thick conducting sheets is:
\[ E = \frac{\sigma}{\epsilon_0} \]