Question

Electric field in a region is given by $\vec{E}=-4 x \hat{i}+6 y \hat{j}$. The charge enclosed in the cube of side $1\, m$ oriented as shown in the diagram is given by $\alpha \in_{0}$. The value of $\alpha$ is___

Answer 1

$\phi=(6 y)$ Area $-(4 x)$ Area $=6 \times 1 \times(1)^{2}$
$-4 \times 1 \times(1)^{2}=2$ therefore $\frac{q}{\varepsilon_{0}}=2 \Rightarrow q=2 \varepsilon_{0}$