Substituting this into Gauss's law and assuming that ε is spatially constant in the region of interest yields ∇ ∇ ⋅ ⋅ E = ρ ρ f ε ε . In electrostatics, we assume that there is no magnetic field (the argument that follows also holds in the presence of a constant magnetic field). Then, we have that ∇ ∇ × × E = 0 , where ∇× is the curl operator. This equation means that we can write the electric field as the gradient of a scalar function φ (called the electric potential), since the curl of any gradient is zero. Thus we can write E = − − ∇ ∇ φ φ , where the minus sign is introduced so that φ is identified as the electric potential energy per unit charge.