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

$ \vec{ E }=2 x ^2 \hat{ i }-4 y \hat{ j }+6 \hat{ k } $

$\phi_{\text {net }}=-8 \times 3+2 \times 6=-12$
$ -12=\frac{ q }{\epsilon_0} $
$ | q |=12 \epsilon_0$