Given : `vecE=(10hati+7hatj)Vm^(-1)`. The electric flux through `1m^(2)` area is XZ plane is

Options

A. 10 Vm
B. 7Vm
C. 100 Vm
D. 49Vm

Explanation

To find the electric flux through a 1 m² area in the xz-plane given the electric field \(\vec{E} = (10 \hat{i} + 7 \hat{j}) \, \text{Vm}^{-1}\), we can follow these steps:

### Step 1: Understand the Area Vector
The area vector for a surface in the xz-plane is directed along the y-axis. Therefore, the area vector \(\vec{A}\) can be expressed as:
\[ \vec{A} = A \hat{j} = 1 \hat{j} \, \text{m}^2 \]

### Step 2: 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:
\[ \Phi = (10 \hat{i} + 7 \hat{j}) \cdot (1 \hat{j}) \]

### Step 3: Compute the Dot Product
The dot product can be computed as follows:
\[ \Phi = (10 \hat{i} \cdot 1 \hat{j}) + (7 \hat{j} \cdot 1 \hat{j}) \]
Since \(\hat{i} \cdot \hat{j} = 0\) (they are perpendicular) and \(\hat{j} \cdot \hat{j} = 1\), we have:
\[ \Phi = 0 + 7 = 7 \, \text{Vm}^2 \]

### Step 4: Conclusion
Thus, the electric flux through the 1 m² area in the xz-plane is:
\[ \Phi = 7 \, \text{Vm}^2 \]