---
tag: 0PKG97PX9Y
kind: concept
name: Conservative vector field
aliases: [gradient-field]
msc: [26B12]
uses: [0299VCW1TH, 0ABK9V9Y64, 0H7C3T1GJY]
sources:
  - url: https://en.wikipedia.org/wiki/Conservative_vector_field
    locator: Definition
same_as:
  wikidata: Q1588205
  wikipedia: Conservative vector field
---

## Summary

A conservative vector field is a [[vector field|0299VCW1TH]] that is the [[gradient|0ABK9V9Y64]] of a scalar function, called a [[scalar potential|0H7C3T1GJY]] of the field.
Its line integrals depend only on the end points of the path, and they vanish around each closed path.