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 \( \sigma \), we can follow these steps:

### Step 1: Understand the Configuration
We have two infinite parallel sheets:
- The first sheet has a uniform charge density \( \sigma \) (positive).
- The second sheet has a uniform charge density \( -\sigma \) (negative).
- The distance between the sheets is \( d \).

### Step 2: Determine the Electric Field due to One Sheet
The electric field \( E \) due to an infinite plane sheet with charge density \( \sigma \) is given by the formula:
\[ E = \frac{\sigma}{2\epsilon_0} \]
where \( \epsilon_0 \) is the permittivity of free space.

### Step 3: Calculate the Electric Field due to Each Sheet
- For the positively charged sheet, the electric field \( E_1 \) at a point between the sheets (directed away from the sheet) is:
\[ E_1 = \frac{\sigma}{2\epsilon_0} \]
- For the negatively charged sheet, the electric field \( E_2 \) at the same point (directed towards the sheet) is:
\[ E_2 = \frac{\sigma}{2\epsilon_0} \]

### Step 4: Combine the Electric Fields
Since the electric fields due to both sheets are in the same direction (towards the negatively charged sheet), we can add them together:
\[ E_{\text{net}} = E_1 + E_2 = \frac{\sigma}{2\epsilon_0} + \frac{\sigma}{2\epsilon_0} \]
\[ E_{\text{net}} = \frac{\sigma}{\epsilon_0} \]

### Step 5: Conclusion
The electric field at a point between the two sheets is:
\[ E_{\text{net}} = \frac{\sigma}{\epsilon_0} \]