1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to find potential function

  1. Aug 13, 2009 #1
    to know that a F is a conservative i need to prove that
    rot [tex]\vec{F}=0[/tex]
    or that grad [tex]U=\vec{F}[/tex]
    [tex]
    \vec{F}=\frac{\vec{r}}{r}
    [/tex]

    how to know U (potential of F)
    ??
     
  2. jcsd
  3. Aug 13, 2009 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Well, if [itex]\textbf{F}=\mathbf{\nabla}U=\partial_x U \hat{x}+\partial_y U \hat{y}+\partial_z U \hat{z}=F_x\hat{x}+F_y\hat{y}+F_z\hat{z}[/itex] (are you familiar with this notation?), then [itex]U=\int F_x dx[/itex], [itex]U=\int F_y dy[/itex] and [itex]U=\int F_z dz[/itex] must all be true. An important note is that in multi-variable calculus, the 'constants' of integration are only constant with respect to the integration variable, so, for example [itex]\int3x^2 dx=x^3+f(y,z)[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook