An electric field, vector E = 2i + 6j + 8k / √ 6 passes through the surface of 4 m^2 area having unit vector

Question

An electric field, \(\vec{E}=\frac{2 \hat{i}\ +\ 6 \hat{j}\ +\ 8 \hat{k}}{\sqrt{6}}\) passes through the surface of \(4 \mathrm{~m}^{2}\) area having unit vector \(\hat{n}=\left(\frac{2 \hat{i}\ +\ \hat{j}\ +\ \hat{k}}{\sqrt{6}}\right)\). The electric flux for that surface is ______\( \mathrm{V} \mathrm{m}\).

Answer 1

Correct answer is : 12 

\(\phi=\vec{E} \cdot \vec{A}\)

\( \begin{aligned} & =\left(\frac{2 \hat{i}+6 \hat{j}+8 \hat{k}}{\sqrt{6}}\right) \cdot 4\left(\frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right) \end{aligned}\)

\( \begin{aligned} & =\frac{4}{6} \times(4+6+8)=12 \mathrm{\ Vm} \end{aligned} \)