Conservative Field:
Conservative fields are vector fields in which the work done by a force is independent of the path taken by the object. This means that the work done in moving an object from one point to another is only dependent on the initial and final positions, not the path taken in between.

Test Charge and Closed Surface:
In the context of electrostatics, a test charge is a small charge placed in an electric field to measure the field's strength at that point. A closed surface is a surface that completely encloses a volume, and the electric field on this surface can be calculated using Gauss's law.

Zero Test Charge around Closed Surface:
If the electric field around any closed surface in a static path is zero, it indicates a conservative field. This is because in a conservative field, the work done in moving a test charge around any closed path is zero. This property is essential in determining the potential energy of a system and simplifying calculations in electrostatics.

Implications of Conservative Fields:
- In a conservative field, the work done in moving a test charge around any closed surface is zero.
- The potential energy of a system in a conservative field only depends on the initial and final positions of the charges.
- Conservative fields simplify calculations in electrostatics as the path taken by the charges does not affect the work done in the system.
In conclusion, a field in which a test charge around any closed surface in a static path is zero is a conservative field. This property is crucial in understanding the behavior of electric fields and simplifying calculations in electrostatics.