Question

can someone explain me what is a conservative vector field

Answer 1

It's one in which the line integral of a closed loop is 0.

Answer 2

Err the integral of the field dotted with the direction vector around the loop rather.

Answer 3

I don't get the physical meaning.Could you please elaborate it??

Answer 4

Think about it like gravity. Gravity is a conservative vector field. At any given point away from the earth, you have a certain amount of force that pulls you in the direction of the earth. If you move away you must expend energy. The amount of energy you use to move away increases your gravitational potential energy, and when you return to the same spot you will have regained that energy in kinetic energy (velocity).