for any volume V containing charge Q. By the relation between charge and charge density, this equation is equivalent to: ∭ ∭ V ∇ ∇ ⋅ ⋅ E d V = ∭ ∭ V ρ ρ ε ε 0 d V for any volume V. In order for this equation to be simultaneously true for every possible volume V, it is necessary (and sufficient) for the integrands to be equal everywhere. Therefore, this equation is equivalent to: