Question

As shown in figure, a cuboid lies in a region with electric field \(E=2 x^2 \hat{i}-4 y \hat{j}+6 \hat{k} N / C\). The magnitude of charge within the cuboid is \(n \epsilon_0 C\). The value of \(n\) is _____. (if dimension of cuboid is \(1 \times 2 \times 3 m ^3\) )

Answer 1

Correct Answer: 12

The correct answer is 12.
$\overrightarrow{E}=2x^2\hat{i}-4y\hat{j}+6\hat{k}$

${\varphi }_{\text{net}}=-8\times 3+2\times 6=-12$
$-12=\frac{q}{{ϵ}_0}$
$|q|=12{ϵ}_0$

So, the answer is 12.