Charge of 2 C is placed at the centre of a cube. What is the electric flux passing through one face ?

Options

A. `(1)/((3 epsi_(0)))`
B. `((1)/(4)) epsi_(0)`
C. `(2)/(epsi_(0))`
D. `(3)/(epsi_(0))`

Answer

To find the electric flux passing through one face of a cube when a charge of 2 C is placed at the center, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Gauss's Law**: According to Gauss's Law, the total electric flux (Φ) through a closed surface is given by the formula:
\[ \Phi = \frac{Q}{\epsilon_0} \]
where \(Q\) is the total charge enclosed and \(\epsilon_0\) is the permittivity of free space.

2. **Identify the Charge**: In this case, the charge \(Q\) is given as 2 C.

3. **Calculate Total Electric Flux**: Using Gauss's Law, we can calculate the total electric flux through the entire surface of the cube:
\[ \Phi = \frac{2 \, \text{C}}{\epsilon_0} \]

4. **Determine the Number of Faces**: A cube has 6 faces. Since the charge is symmetrically placed at the center, the electric flux will be uniformly distributed across all faces.

5. **Calculate Flux Through One Face**: To find the electric flux through one face of the cube, we divide the total electric flux by the number of faces:
\[ \Phi_{\text{one face}} = \frac{\Phi}{6} = \frac{2 \, \text{C}}{6 \epsilon_0} = \frac{1}{3 \epsilon_0} \]

6. **Conclusion**: The electric flux passing through one face of the cube is:
\[ \Phi_{\text{one face}} = \frac{1}{3 \epsilon_0} \]

### Final Answer:
The electric flux passing through one face of the cube is \(\frac{1}{3 \epsilon_0}\).