If an electric field is given by `10hati+3hatj+4hatk` calculate the electric flux through a surface of area 10 units lying in yz plane

Options

A. 100 units
B. 10 units
C. 30 units
D. 40 units

Answer

To calculate the electric flux through a surface of area 10 units lying in the yz-plane when the electric field is given by \( \vec{E} = 10 \hat{i} + 3 \hat{j} + 4 \hat{k} \), we can follow these steps:

### Step 1: Understand the Geometry
The yz-plane is defined as the plane where the x-coordinate is constant (x = 0). The area vector \( \vec{A} \) for a surface lying in the yz-plane points in the direction of the x-axis, which is along \( \hat{i} \).

### Step 2: Define the Area Vector
Since the area of the surface is 10 units and it lies in the yz-plane, the area vector can be expressed as:
\[ \vec{A} = A \hat{i} = 10 \hat{i} \]

### Step 3: Calculate the Electric Flux
The electric flux \( \Phi \) through a surface is given by the dot product of the electric field \( \vec{E} \) and the area vector \( \vec{A} \):
\[ \Phi = \vec{E} \cdot \vec{A} \]
Substituting the values:
\[ \Phi = (10 \hat{i} + 3 \hat{j} + 4 \hat{k}) \cdot (10 \hat{i}) \]

### Step 4: Compute the Dot Product
The dot product can be calculated as follows:
\[ \Phi = 10 \cdot 10 + 3 \cdot 0 + 4 \cdot 0 = 100 + 0 + 0 = 100 \]

### Step 5: Conclusion
The electric flux through the surface is:
\[ \Phi = 100 \, \text{units} \]