Question

if tje circulation of a vector field is a given point is zero , can we say its curl is zero or its divergence is zero and why?

Answer 1

To understand the basic answer for this question lets first understand what is circulation of vector field at a point- Circulation of vector field at a point means tendency of particles to rotate about the axis at that points in the direction of the curl.

The name divergence means how much field spread from the point of its spread ,So that a vector field in its connected domain is conservative when its curl is zero, which simply means that it has not any curling field or we can say circulation of its field like a magnetic field and as here it is given that, circulation of a vector field at a point is zero which means it is a divergent vector field like an electric field and when we find its curl we will get it will give us zero as it is a divergent field so curling is not possible.

Hence we can say that its curl or its divergence is zero.