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!

Divergence of a Magnetic Field not equaling zero

  1. Feb 1, 2013 #1
    I have a larger problem involving divergences and curls, but the correct answer requires ∇°B (divergence of B) = 0. I understand the proof of this in Griffiths, but the definition of divergence in cylindrical coordinates is:

    be94b3e55572cfa8cb0fe2a048324766.png

    After using the product rule to split the first term, we get the divergence of B is B_rho / rho + 0 + 0 + 0, or simply Div(B)=B_rho / rho; however, this clearly contradicts what we know about the divergence of B being zero. Can someone please clarify this for me, I've been stuck at it for hours.

    Thanks.

    P.s. First post!
     
  2. jcsd
  3. Feb 1, 2013 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    How do you know that the partial derivatives you claim to be zero are zero? Do you have a specific field in mind? A field that's a constant vector in Cartesian can look rather different in polar.
     
  4. Feb 1, 2013 #3
    Thank you haruspex for responding. The partial derivatives I said equal zero could be my mistake, but please explain how a vector with constant components in cartesian coordinates can have nonzero partial derivatives in cylindrical coordinates.
     
  5. Feb 1, 2013 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Aρ, for example, refers to the component of the vector in the ρ direction. If the vector is constant, its component in the ρ direction may yet depend on θ and z. It's not that the vector varies, but that the unit ρ-direction vector does.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook