According to Maxwell's equations, an electric field (u, v) in two space dimensions that is independent of time satisfies ∇ × ( u , v , 0 ) = ( v x − u y ) k ^ = 0 , {\displaystyle \nabla \times (u,v,0)=(v_{x}-u_{y}){\hat {\mathbf {k} }}=\mathbf {0} ,} and ∇ ⋅ ( u , v ) = ρ , {\displaystyle \nabla \cdot (u,v)=\rho ,} where ρ is the charge density.
De acordo ás ecuacións de Maxwell, un campo eléctrico (u,v) nun espazo de dúas dimensións que é independente do tempo satisfai { ∇ × ( u , v ) = v x − u y = 0 , ∇ ⋅ ( u , v ) = ρ , {\displaystyle {\begin{cases}\nabla \times (u,v)=v_{x}-u_{y}=0,\,\\\nabla \cdot (u,v)=\rho ,\,\end{cases}}} onde ρ {\displaystyle \rho } é a densidade de carga.