Question

In a region of space, the electric field is given by $\overrightarrow{E}=8\hat{i}+4\hat{j}+3\hat{k}$. The electric flux through a surface of area of $100\text{units}$ in $x-y$ plane is

• A. $400\text{units}$
• B. $800\text{units}$
• C. $300\text{units}$
• D. $1500\text{units}$

Answer 1

The correct option is C $300\text{units}$

Given,
Electric field vector, $\overrightarrow{E}=8\hat{i}+4\hat{j}+3\hat{k}$

As , the plane surface is parallel to $\text{x-y}$plane, so the area vector $\overrightarrow{A}$ points along the positive direction of $\text{z-}$axis.
So, area vector, $\overrightarrow{A}=100\hat{k}$

Electric flux through the surface,
$\varphi =\overrightarrow{E}.\overrightarrow{A}$

$\Rightarrow \varphi =(8\hat{i}+4\hat{j}+3\hat{k}).\left(100\hat{k}\right)$

$\therefore \varphi =300\text{units}$

Hence, option (b) is the correct answer.