both conservative and solenoidal vector fieldby aruna1 Tags: conservative, field, solenoidal, vector 

#1
Nov1208, 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 



#2
Nov1208, 07:43 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,900

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.




#3
Nov1208, 08:42 AM

P: 111

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 threedimensional vector field is conservative  Calculus & Beyond Homework  6  
divergence and solenoidal vector fields  General Math  8 