Assume the domain of each of the vector fields pictured is R². Which, if any, of the vector fields are conservative? Which, if any, have divergence-0 (everywhere in the plane). Justify your answer.
A vector field is not conservative if one can find a closed path around which the circulation of the vector field is not zero.
We know that, a conservative vector field is the gradient of the potential function. This means if we can draw level curves satisfying that every vector is perpendicular to level curve and the level curves are closer where the magnitude of vector field is large then we can say that the vector field is conservative.
The divergence of a vector field can be seen a flow of fluid. If the fluid inflow into a circle is less when compared to fluid outflow of the circle then the divergence is positive, otherwise negative or zero. If the flow inside is equal to flow outside then the divergence is zero.
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