Question

If the electric flux through a surface of area $100m^2$ lying in the $x-y$ plane is $p\sqrt{q}Vm$ then find $pq$. Given $\overrightarrow{E}=\hat{i}+\sqrt{2}\hat{j}+\sqrt{3}\hat{k}$

Answer 1

We know that electric flux is:
$\varphi =\overrightarrow{E}.\overrightarrow{S}$
Given $\overrightarrow{E}=\hat{i}+\sqrt{2}\hat{j}+\sqrt{3}\hat{k}$
$\overrightarrow{S}=100m^2\hat{k}$
$\varphi =(\hat{i}+\sqrt{2}\hat{j}+\sqrt{3}\hat{k}).\left(100\hat{k}\right)$
$=100\sqrt{3}Vm$
From questtion $\varphi =(p\sqrt{q}$Vm)
By comparing, we get
$p=100$ and $q=3$
Hence, $pq=300$.