Are all constant fields conservative? Can there be some constant vector fields which are not conservative?
2026-03-25 05:48:44.1774417724
Are all constant fields conservative?
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The answer is affirmative. A conservative field is a vector field which is the gradient of some function. So, if $\mathbf v$ is a constant vector field, that is $\mathbf{v}(x_1,\ldots,x_n)=(a_1,\ldots,a_n)$, you can take$$F(x_1,\ldots,x_n)=a_1x_1+\cdots+a_nx_n.$$Then $\mathbf{v}=\nabla F$.