The electric field near a conducting surface having a uniform surface charge denstiy `sigma` is given by

Options

A. (a) `(sigma)/(epsi_(0))` and is parallel to the surface
B. (b) `(2 sigma)/(epsi_(0))`
C. (c) `(sigma)/(epsi_(0))` and is normal to the surface
D. (d) `(2 sigma)/(epsi_(0))` and is normal to the surface

Answer

To solve the problem of finding the electric field near a conducting surface with a uniform surface charge density \( \sigma \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have a conducting surface with a uniform surface charge density \( \sigma \). We need to determine the electric field \( E \) near this surface.

2. **Choosing a Gaussian Surface**:
To apply Gauss's law, we will consider a Gaussian surface. A suitable choice is a cylindrical Gaussian surface that straddles the conducting surface. This surface will have one flat face inside the conductor and one flat face outside.

3. **Applying Gauss's Law**:
According to Gauss's law, the electric flux \( \Phi_E \) through a closed surface is equal to the charge enclosed \( Q \) divided by the permittivity of free space \( \epsilon_0 \):
\[ \Phi_E = \frac{Q}{\epsilon_0} \]
The electric flux \( \Phi_E \) is given by:
\[ \Phi_E = E \cdot A \]
where \( E \) is the electric field and \( A \) is the area of the Gaussian surface.

4. **Calculating the Charge Enclosed**:
The charge \( Q \) enclosed by the Gaussian surface can be calculated using the surface charge density \( \sigma \):
\[ Q = \sigma \cdot A \]

5. **Setting Up the Equation**:
Substituting the expression for \( Q \) into Gauss's law gives:
\[ E \cdot A = \frac{\sigma \cdot A}{\epsilon_0} \]

6. **Solving for the Electric Field \( E \)**:
We can cancel \( A \) from both sides (assuming \( A \neq 0 \)):
\[ E = \frac{\sigma}{\epsilon_0} \]

7. **Direction of the Electric Field**:
The electric field \( E \) is directed perpendicular to the surface of the conductor and away from the surface if the charge is positive.

### Final Answer:
The electric field near a conducting surface having a uniform surface charge density \( \sigma \) is given by:
\[ E = \frac{\sigma}{\epsilon_0} \]