A force \(\mathop \to \limits_F \) is acting on a particle whose potential energy is \(U\left( {\mathop \to \limits_r } \right)\) at a point \(\mathop \to \limits_r \). If it is a conservative force then -
1
\(\mathop \to \limits_\nabla \cdot \mathop \to \limits_{\rm{F}} = 0\)
2
\(\mathop \to \limits_\nabla \times \mathop \to \limits_F = 0\)
3
\(\mathop \to \limits_\nabla \left( {\mathop \to \limits_{\rm{F}} } \right) = 0\)
4
\(\mathop \to \limits_\nabla \times \mathop \to \limits_F = \nabla {\rm{U}}\left( {\mathop \to \limits_{\rm{r}} } \right)\)