both conservative and solenoidal vector field

aruna1

1. The problem statement, all variables and given/known data

if a vecor A is both solenoidal and conservative; is it correct that

A=-▼Φ

that is

A=- gradΦ

Φ is a scalar function

thanks

HallsofIvy

If A is just a conservative vector field, then [itex]A= -\nabla \phi[/itex] for some scalar function [itex]\phi[/itex]. I'm not sure what requiring that it also be solenoidal adds.

aruna1

Quote by HallsofIvy

If A is just a conservative vector field, then [itex]A= -\nabla \phi[/itex] for some scalar function [itex]\phi[/itex]. I'm not sure what requiring that it also be solenoidal adds.

well i thouhgt if A is only conservative
then

[itex]A= \nabla \phi[/itex] (according to my text book)

not

[itex]A= -\nabla \phi[/itex]

so what is right?

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aruna1	both conservative and solenoidal vector field Tweet 1. The problem statement, all variables and given/known data if a vecor A is both solenoidal and conservative; is it correct that A=-▼Φ that is A=- gradΦ Φ is a scalar function thanks

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	If A is just a conservative vector field, then [itex]A= -\nabla \phi[/itex] for some scalar function [itex]\phi[/itex]. I'm not sure what requiring that it also be solenoidal adds.