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!

Why does this say ∇-∇Φ=∇^2Φ?

  1. Jan 16, 2015 #1
    Hey all, in this line of a proof it went straight from
    ∇-∇Φ=-4πGρ to
    ∇^2Φ=4πGρ
    ∇ is divergence, Φ is supposed to be potential energy.
    G is gravitational constant and p is density so both are scalars, Any help apreciated.
     
  2. jcsd
  3. Jan 16, 2015 #2

    jedishrfu

    Staff: Mentor

  4. Jan 16, 2015 #3
    "gradient of the function Phi is the laplacian of the function Phi" So ∇Φ=∇^2Φ? but then why the ∇-∇Φ=∇^2Φ?
     
  5. Jan 16, 2015 #4

    mathman

    User Avatar
    Science Advisor
    Gold Member

    You misread the previous post. It says "divergence of the gradient is the Laplacian". Don't omit "divergence of".
     
  6. Jan 17, 2015 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I believe you are mis-reading. A "[itex]\nabla[/itex]" by itself does not have any meaning and [itex](\nabla- \nabla)\phi[/itex] would be equal to 0.

    I suspect that what you are reading as "-", a subtraction, is really "[itex]\cdot[/itex]", a dot product. [itex]\nabla^2 \phi[/itex] is defined as [itex]\nabla\cdot \nabla \phi[/itex].
     
  7. Jan 28, 2015 #6
    Brilliant! thank you so much, wow I cannot believe I didn't see that, wow.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Why does this say ∇-∇Φ=∇^2Φ?
  1. Why does this work? (Replies: 4)

  2. Why does a = -a? (Replies: 3)

Loading...