Given an electric field `E= 2 xx 10^3 N//C` is along the X – axis and passing through a square of an area s `= 10^(-2) m^2`. If the line normal to the square plane makes a `60^@` angle with the X - axis, find the flux through the square:

Options

A. `30 N C^(-1) m^2`
B. `10 N C^(-1) m^2`
C. `20 N C^(-1) m^2`
D. `25 N C^(-1) m^2`

Explanation

To find the electric flux through the square, we can use the formula for electric flux (Φ) given by:

\[ Φ = E \cdot A \cdot \cos(θ) \]

where:
- \(E\) is the magnitude of the electric field,
- \(A\) is the area of the surface,
- \(θ\) is the angle between the electric field and the normal to the surface.

### Step 1: Identify the values
- Given electric field, \(E = 2 \times 10^3 \, \text{N/C}\)
- Area of the square, \(A = 10^{-2} \, \text{m}^2\)
- Angle, \(θ = 60^\circ\)

### Step 2: Calculate the cosine of the angle
We need to find \(\cos(60^\circ)\):
\[ \cos(60^\circ) = \frac{1}{2} \]

### Step 3: Substitute the values into the flux formula
Now, substituting the values into the flux formula:
\[ Φ = E \cdot A \cdot \cos(θ) \]
\[ Φ = (2 \times 10^3 \, \text{N/C}) \cdot (10^{-2} \, \text{m}^2) \cdot \left(\frac{1}{2}\right) \]

### Step 4: Perform the calculations
Calculating the flux:
\[ Φ = (2 \times 10^3) \cdot (10^{-2}) \cdot \left(\frac{1}{2}\right) \]
\[ Φ = (2 \cdot 10^3 \cdot 10^{-2}) \cdot \frac{1}{2} \]
\[ Φ = (2 \cdot 10^{1}) \cdot \frac{1}{2} \]
\[ Φ = 10 \cdot \frac{1}{2} \]
\[ Φ = 5 \, \text{N m}^2/\text{C} \]

### Final Answer
The electric flux through the square is:
\[ Φ = 5 \, \text{N m}^2/\text{C} \]