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 Area Vector
The surface lies in the yz-plane, which means the area vector \( \vec{A} \) will be perpendicular to the surface and directed along the x-axis. The area of the surface is given as 10 units. Therefore, the area vector can be expressed as:
\[ \vec{A} = 10\hat{i} \]

### Step 2: Write the Electric Field Vector
The electric field vector is given as:
\[ \vec{E} = 10\hat{i} + 3\hat{j} + 4\hat{k} \]

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

### Step 4: Perform the Dot Product
The dot product can be calculated as follows:
\[ \Phi_E = (10)(10) + (3)(0) + (4)(0) = 100 + 0 + 0 = 100 \]

### Step 5: Final Result
Thus, the electric flux through the surface is:
\[ \Phi_E = 100 \text{ units} \]

### Summary
The electric flux through the surface of area 10 units lying in the yz-plane is 100 units.

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