Electric field intensity at a point due to an infinite sheet of charge having surface charge density `sigma` is `E`.If sheet were conducting electric intensity would be

Options

A. `E//2`
B. `E`
C. `2E`
D. `4E`

Answer

To find the electric field intensity at a point due to an infinite conducting sheet of charge with surface charge density \( \sigma \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Electric Field due to an Infinite Sheet of Charge**:
The electric field intensity \( E \) due to an infinite sheet of charge with surface charge density \( \sigma \) is given by the formula:
\[ E = \frac{\sigma}{2 \epsilon_0} \]
where \( \epsilon_0 \) is the permittivity of free space.

2. **Behavior of Conductors in Electrostatics**:
When a sheet is conducting, the charges will redistribute themselves on the surface of the conductor. For a conducting sheet with surface charge density \( \sigma \), the positive charges will accumulate on the surface.

3. **Effect of Both Surfaces of the Conducting Sheet**:
Since the conducting sheet has two surfaces, each surface will create its own electric field. The electric field due to one side of the sheet will be \( \frac{\sigma}{2 \epsilon_0} \) directed away from the sheet. Therefore, the total electric field due to both surfaces will be:
\[ E_{\text{total}} = E_{\text{left}} + E_{\text{right}} = \frac{\sigma}{2 \epsilon_0} + \frac{\sigma}{2 \epsilon_0} = \frac{\sigma}{\epsilon_0} \]

4. **Direction of the Electric Field**:
The electric field will point away from the positively charged surfaces of the conducting sheet. Hence, the direction of the electric field will be perpendicular to the surface of the sheet.

5. **Final Result**:
Therefore, the electric field intensity \( E \) at a point due to an infinite conducting sheet with surface charge density \( \sigma \) is:
\[ E = \frac{\sigma}{\epsilon_0} \]

### Summary:
The electric field intensity at a point due to an infinite conducting sheet of charge with surface charge density \( \sigma \) is \( E = \frac{\sigma}{\epsilon_0} \).