Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Determination of electric field E

  1. Aug 30, 2013 #1
    Theorem in electromagnetism says if the divergence [itex]\nabla\cdot E[/itex] and the curl [itex]\nabla\times E[/itex] are known, then E is uniquely determined. So my question is, the divergence equation gives 1 constraint and the curl equation gives 3 constraints, which add up to 4 constraints. On the other hand, the electric filed E has only 3 unknown components. Does it mean 4 equations are overdetermined and thus has dependency?
     
  2. jcsd
  3. Aug 31, 2013 #2

    Jano L.

    User Avatar
    Gold Member

    If the system of equations is overdetermined, it means there is no solution.

    If the equations are dependent, it means one or more equations are superfluous (do not give new constraint).

    Divergence and curl of a field are both necessary to reconstruct the field. See

    http://mathworld.wolfram.com/HelmholtzsTheorem.html
     
  4. Aug 31, 2013 #3

    Dale

    Staff: Mentor

    You might like this paper

    http://faculty.uml.edu/cbaird/95.657(2013)/Maxwell_Uniqueness.pdf
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook