# Physical interpretation of $\iiint (∇\cdot\vec E)\mbox{d} V$ [duplicate]

1. Can anybody explain the physical interpretation of Gauss's law $$\iiint (\nabla\cdot \vec E)~\mbox{d}V~=~\frac{Q}{\epsilon_0}?$$

2. Also, how is the differential form of Gauss's law obtained from the integral form?

3. How can volume multiplied by a gradient equals flux through a closed surface?

$$\nabla\cdot\vec E =\frac{q}{\epsilon_0}$$