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Both conservative and solenoidal vector field

by aruna1
Tags: conservative, field, solenoidal, vector
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aruna1
#1
Nov12-08, 07:19 AM
P: 111
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
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HallsofIvy
#2
Nov12-08, 07:43 AM
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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
#3
Nov12-08, 08:42 AM
P: 111
Quote Quote by HallsofIvy View Post
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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