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. `2E`
B. `E`
C. `E/2`
D. none of these

Answer

To solve the problem of finding the electric field intensity at a point due to an infinite conducting sheet of charge, we can follow these steps:

### Step 1: Understand the Electric Field due to an Infinite Sheet of Charge
For an infinite sheet of charge with surface charge density \( \sigma \), the electric field intensity \( E \) at a point near the sheet is given by the formula:
\[ E = \frac{\sigma}{2\epsilon_0} \]
where \( \epsilon_0 \) is the permittivity of free space.

### Step 2: Consider the Conducting Sheet
When the sheet is a conductor, the charges will redistribute themselves on the surface of the conductor. For an infinite conducting sheet, the charge will be distributed uniformly on both sides of the sheet.

### Step 3: Apply Gauss's Law
To find the electric field due to the conducting sheet, we can use Gauss's Law. The electric field due to each side of the conducting sheet is:
\[ E_{\text{one side}} = \frac{\sigma}{2\epsilon_0} \]
Since the conducting sheet has charges on both sides, the total electric field \( E_{\text{total}} \) at a point outside the conducting sheet will be:
\[ E_{\text{total}} = E_{\text{one side}} + E_{\text{one side}} = \frac{\sigma}{2\epsilon_0} + \frac{\sigma}{2\epsilon_0} = \frac{\sigma}{\epsilon_0} \]

### Step 4: Relate the Electric Field of the Conducting Sheet to the Original Electric Field
From our earlier step, we know that the electric field \( E \) due to the infinite sheet of charge is:
\[ E = \frac{\sigma}{2\epsilon_0} \]
Thus, the electric field due to the conducting sheet can be expressed as:
\[ E_{\text{conducting}} = 2E \]

### Step 5: Conclusion
Therefore, the electric field intensity at a point due to an infinite conducting sheet of charge is:
\[ E_{\text{conducting}} = 2E \]

### Final Answer
The electric field intensity if the sheet were conducting would be \( 2E \).

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