Electric field intensity at a point in between two parallel sheets with like charges of same surface charge densities `(sigma)` is

Options

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

Answer

To find the electric field intensity at a point between two parallel sheets with like charges of the same surface charge density (σ), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Configuration**:
We have two parallel sheets, both having the same surface charge density (σ). The sheets can either be both positively charged or both negatively charged.

2. **Electric Field Due to a Single Sheet**:
The electric field (E) due to an infinite plane sheet with surface charge density σ is given by the formula:
\[ E = \frac{\sigma}{2\epsilon_0} \]
where ε₀ is the permittivity of free space.

3. **Direction of Electric Field**:
- If the sheets are positively charged, the electric field due to each sheet points away from the sheet.
- If the sheets are negatively charged, the electric field due to each sheet points towards the sheet.

4. **Calculating the Electric Field Between the Sheets**:
- For two positively charged sheets:
- The electric field due to the first sheet (E₁) at a point between the sheets points away from the sheet.
- The electric field due to the second sheet (E₂) also points away from it.
- Therefore, both fields add up in the region between the sheets:
\[ E_{\text{net}} = E_1 + E_2 = \frac{\sigma}{2\epsilon_0} + \frac{\sigma}{2\epsilon_0} = \frac{\sigma}{\epsilon_0} \]

- For two negatively charged sheets:
- The electric field due to the first sheet points towards it.
- The electric field due to the second sheet also points towards it.
- Thus, the fields again add up in the region between the sheets:
\[ E_{\text{net}} = E_1 + E_2 = \frac{\sigma}{2\epsilon_0} + \frac{\sigma}{2\epsilon_0} = \frac{\sigma}{\epsilon_0} \]

5. **Conclusion**:
Since both cases (positive and negative charges) yield the same result, we conclude that the electric field intensity at a point between two parallel sheets with like charges of the same surface charge density is:
\[ E_{\text{net}} = \frac{\sigma}{\epsilon_0} \]

### Final Answer:
The electric field intensity at a point between two parallel sheets with like charges of the same surface charge density (σ) is:
\[ E = \frac{\sigma}{\epsilon_0} \]