If there is no scalar function V in such a way that \( \vec{F}=-\vec{\nabla}V \), i.e. the force cannot be expressed as the gradient of a scalar function, then the force acting on the particle is called the non-conservative force.
A force \( \vec{F} \) acting on a particle is said to non-conservative if the curl of the force is not zero, i.e. \( \vec{\nabla}\times{\vec{F}}\neq{0} \).
A force \( \vec{F} \) acting on a particle is said to be non-conservative if the work by the force in moving that particle from the initial point to the final point depends upon the actual path.
