A cube is arranged such that its length, breadth and height are along X, Y and Z directions, One of its corners is situated a the origin. Length of each side of the cube is 25cm. The components of electric field are `E_(x) = 400 sqrt2 N//C, E_(y) = 0 and E_(z)= 0` respectively. Find the flux coming out of the cube at one end.

Options

A. 25
B. `(25)/(sqrt2)`
C. `25 sqrt2`
D. zero

Answer

To find the electric flux coming out of one end of the cube, we can use Gauss's law, which states that the electric flux (Φ) through a surface is given by the product of the electric field (E) and the area (A) of the surface through which the field lines are passing. The formula for electric flux is:

\[ \Phi = E \cdot A \]

### Step-by-step Solution:

1. **Identify the dimensions of the cube**:
The length of each side of the cube is given as 25 cm. Convert this to meters for consistency in SI units:
\[ \text{Side length} = 25 \text{ cm} = 0.25 \text{ m} \]

2. **Determine the area of one face of the cube**:
Since the cube has square faces, the area \(A\) of one face is given by:
\[ A = \text{side}^2 = (0.25 \text{ m})^2 = 0.0625 \text{ m}^2 \]

3. **Identify the electric field components**:
The components of the electric field are given as:
\[ E_x = 400 \sqrt{2} \text{ N/C}, \quad E_y = 0, \quad E_z = 0 \]
Since the electric field has no components in the y and z directions, we only consider \(E_x\) for the flux through the face normal to the x-axis.

4. **Calculate the electric flux through the face normal to the x-axis**:
The electric flux through the face of the cube that is normal to the x-axis can be calculated using the formula:
\[ \Phi = E_x \cdot A \]
Substituting the values:
\[ \Phi = (400 \sqrt{2} \text{ N/C}) \cdot (0.0625 \text{ m}^2) \]

5. **Perform the calculation**:
First, calculate \(400 \cdot 0.0625\):
\[ 400 \cdot 0.0625 = 25 \]
Now, multiply by \(\sqrt{2}\):
\[ \Phi = 25 \sqrt{2} \text{ Nm}^2/\text{C} \]

### Final Answer:
The electric flux coming out of the cube at one end is:
\[ \Phi = 25 \sqrt{2} \text{ Nm}^2/\text{C} \]