both conservative and solenoidal vector field


by aruna1
Tags: conservative, field, solenoidal, vector
aruna1
aruna1 is offline
#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
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
HallsofIvy
HallsofIvy is offline
#2
Nov12-08, 07:43 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,886
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
aruna1 is offline
#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?


Register to reply

Related Discussions
Conservative vector field or not? Calculus & Beyond Homework 9
Conservative vector field; classification of derivative Differential Geometry 1
Conservative vector field, potential function Calculus & Beyond Homework 5
Showing that a three-dimensional vector field is conservative Calculus & Beyond Homework 6
divergence and solenoidal vector fields General Math 8