Answer:
From the given information we can infer that the field is not conservative.
Explanation:
For a conservative field the work done on an object in moving it from a position given by co-ordinates [tex](x_{1},y_{1},z_{1})[/tex] to another position with co-ordinates [tex](x_{2},y_{2},z_{2})[/tex] shall be independent of the path we take in between to reach our final position (by definition of a conservative field). But in the given case since the initial and the final position of both the curves [tex]C_{1},C_{2}[/tex] coincide but the work done along both the paths is different thus we conclude that the field is not conservative.