Electric flux through a surface element `dvecS = 4hati` placed in an electric field `vecE = (5hati+4hatj +9hatk)`, is:

Options

A. 20 units
B. 40 units
C. 16 units
D. 36 units

Explanation

To find the electric flux through the surface element \( d\vec{S} \) placed in the electric field \( \vec{E} \), we will use the formula for electric flux:

\[ \Phi_E = \vec{E} \cdot d\vec{S} \]

### Step 1: Identify the vectors
Given:
- Electric field \( \vec{E} = 5\hat{i} + 4\hat{j} + 9\hat{k} \)
- Surface element \( d\vec{S} = 4\hat{i} \)

### Step 2: Calculate the dot product
To find the electric flux, we need to calculate the dot product \( \vec{E} \cdot d\vec{S} \):

\[ \vec{E} \cdot d\vec{S} = (5\hat{i} + 4\hat{j} + 9\hat{k}) \cdot (4\hat{i}) \]

Using the dot product formula, we can expand this:

\[ \vec{E} \cdot d\vec{S} = 5 \cdot 4 + 4 \cdot 0 + 9 \cdot 0 \]

### Step 3: Simplify the expression
Now, simplify the expression:

\[ \vec{E} \cdot d\vec{S} = 20 + 0 + 0 = 20 \]

### Step 4: Conclusion
Thus, the electric flux through the surface element is:

\[ \Phi_E = 20 \text{ units} \]