Two infinite plane parallel sheets, separated by a distance d have equal and opposite uniform charge densities `sigma`. Electric field at a point between the sheets is

Options

A. `(sigma)/(2epsilon_(0))`
B. `(sigma)/(epsilon_(0))`
C. zero
D. depends on the location of the point

Explanation

To find the electric field at a point between two infinite parallel sheets with equal and opposite uniform charge densities (σ), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- We have two infinite parallel sheets. Let’s denote the first sheet as Sheet 1 with a positive charge density (+σ) and the second sheet as Sheet 2 with a negative charge density (-σ).
- The distance between the sheets is given as \( d \).

2. **Electric Field Due to a Single Infinite Sheet**:
- The electric field \( E \) due to an infinite sheet with uniform charge density \( \sigma \) is given by the formula:
\[ E = \frac{\sigma}{2\epsilon_0} \]
- The direction of the electric field produced by a positively charged sheet is away from the sheet, while for a negatively charged sheet, it is towards the sheet.

3. **Calculating the Electric Fields**:
- For Sheet 1 (positively charged):
- The electric field \( E_1 \) is directed away from the sheet, and its magnitude is:
\[ E_1 = \frac{\sigma}{2\epsilon_0} \]
- For Sheet 2 (negatively charged):
- The electric field \( E_2 \) is directed towards the sheet, and its magnitude is:
\[ E_2 = \frac{\sigma}{2\epsilon_0} \]

4. **Direction of the Electric Fields**:
- Since \( E_1 \) is directed to the right (away from Sheet 1) and \( E_2 \) is also directed to the right (towards Sheet 2), both electric fields in the region between the sheets add up.

5. **Total Electric Field Between the Sheets**:
- The total electric field \( E \) at a point between the sheets is the sum of the magnitudes of \( E_1 \) and \( E_2 \):
\[ E = E_1 + E_2 = \frac{\sigma}{2\epsilon_0} + \frac{\sigma}{2\epsilon_0} = \frac{\sigma}{\epsilon_0} \]

6. **Conclusion**:
- The electric field at a point between the sheets is:
\[ E = \frac{\sigma}{\epsilon_0} \]

### Final Answer:
The electric field at a point between the sheets is \( \frac{\sigma}{\epsilon_0} \).

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