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!

I Gradient of displacement vector

  1. Mar 9, 2016 #1
    I have a quantity defined as ## r =
    \left|\vec{r} - \vec{r'}
    ## and am trying to take the gradient of this quantity. Now the gradient is with respect to the ordinary vector, ## \vec{r}##, and not ## \vec{r'} ##. But after looking at a solution, it says the direction of the gradient is in the direction parallel to ## \vec{r} - \vec{r'} ## and not ## \vec{r} ##. My apologies for being a bit vague here, but shouldn't the direction of the gradient be pointing in the direction in which the derivative is being taken (assuming only a radial component exists)? So if I am taking the derivative with respect to ## r ##, then it points in a direction parallel to ## \vec{r}##, while a derivative wrt to ##r - r' ## would point in ## \vec{r} - \vec{r'} ##?
  2. jcsd
  3. Mar 9, 2016 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member
    2017 Award

    No, you are wrong. I suggest actually doing the math rather than trying to reason your way forward.

    If you definitely want to reason, you should use a translation argument from the gradient of the distance from the origin.
  4. Mar 9, 2016 #3
    you should write out the equation in Cartesian coordinate
  5. Mar 10, 2016 #4
    If you want to see why direction of the gradient does not have to be in the direction in which derivative is taken, here is an intuitive argument:
    Gradient of a scalar function means that the direction in which the function changes most. So when you change r infinitesimally the change in the magnitude of the displacement vector cannot be independent of the direction of the r' because it affects the displacement vector.
    Also, if you write it mathematically you will encounter a term like rr'cosa where a is the angle between r and r'. So you cannot assume there is no angular dependency.
    Last edited: Mar 10, 2016
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Gradient displacement vector Date
I Understanding Gauss' law: diff b/w E and D flux? Oct 25, 2017
I Pressure Gradients along an angle pipe Dec 20, 2016
I How to take the time derivative of a potential gradient ? Dec 2, 2016