Question

If $\overrightarrow{E}=\hat{i}+\sqrt{2}\hat{j}+\sqrt{3}\hat{k}$, then find the Electric flux through surface of area $100{\text{m}}^2$ lying in the $\text{xy-plane}$ (in $\text{Vm}$)

• A. $100$
• B. $141.4$
• C. $173.2$
• D. $200$

Answer 1

The correct option is C $173.2$

Given,

Electric field vector, $\overrightarrow{E}=(\hat{i}+\sqrt{2}\hat{j}+\sqrt{3}\hat{k})$

For, $\text{xy-plane}$ area vector is along $\hat{k}$.

So, $\overrightarrow{A}=100\hat{k}{\text{m}}^2$

So, for constant electric field, electric flux through the surface is given by $$\varphi =\overrightarrow{E}.\overrightarrow{A}$$ $\Rightarrow \varphi =(\hat{i}+\sqrt{2}\hat{j}+\sqrt{3}\hat{k}).\left(100\hat{k}\right)$

$\Rightarrow \varphi =100\sqrt{3}$

$\therefore \varphi \approx 173.2$

Hence, option (c) is the correct answer.