Del Operator

  1. Hello All,

    May I know what is the difference between
    1) Del operator with respect for field point
    2) Del operator with respect to source point

  2. jcsd
  3. newbie,

    Not sure what you mean.

    Del is an operation on a scalar that gives a vector (namely, the gradient of the scalar)

    What are the "field" and "source" that you're talking about?
  4. arildno

    arildno 11,265
    Science Advisor
    Homework Helper
    Gold Member

    I am quite certain that he is confused by the convention of regarding the divergence of a source potential as a multiple of dirac's delta function.

    However, only newbie knows for sure..
  5. Hi All,

    thanks for helping.. let me explain
    i'm reading this text on the derivation of helmholtz theorem

    let me just quote directly from the book



    Page 2 top half
    " In Equations (A-2) through (A-5), the operator 'del-f' differentiates with respect to field point rf, while the operator 'del-s' differentiates with repect to the source point rs"

    May I know the difference between the operators here.

    Page 2 bottom half
    " From Equation (A-1) since F(rs) is a function of the source point alone, but "del-f" differentiates with respect to the field point.... "

    Well apparently we can move F(rs) out of the lapacian here. Please help explain how this is possible

    thanks again
    Last edited: Apr 20, 2005
  6. jtbell

    Staff: Mentor

    That means that, for example,

    [tex]\nabla_f V = \frac {\partial V}{\partial x_f} \hat {\bold i} + \frac {\partial V}{\partial y_f} \hat {\bold j} + \frac {\partial V}{\partial z_f} \hat {\bold k} [/tex]


    [tex]\nabla_s V = \frac {\partial V}{\partial x_s} \hat {\bold i} + \frac {\partial V}{\partial y_s} \hat {\bold j} + \frac {\partial V}{\partial z_s} \hat {\bold k} [/tex]

    where V is some function of [itex]x_f[/itex], [itex]y_f[/itex], [itex]z_f[/itex], [itex]x_s[/itex], [itex]y_s[/itex], and [itex]z_s[/itex] (that is, depends on both the field coordinates and the source coordiates).
  7. jtbell,

    So your vector V is analogous to the Green's function G(rs,rf) since it's a function of both rs and rf. But since F(rs) is a function only of rs, it doesn't vary with rf, so when derivatives are taken wrt rf, F acts like a constant.

    newbie, does that help at all, or am I missing your point entirely?
  8. jtbell & jdavel,

    yes it does explain everything if vector V here is a function of both (x,y,z) at field point and (x,y,z) at source point.... which should be the case

    since the E field at a point would depend on both
    1) where the field point is as well as
    2) where the source is

    however, im still not understanding the partial derivative here ... i mean how is dV/dXf different from dV/dXs ... arent there only 3 axis here X,Y,Z so the gradient whould still be the same wouldnt it ???

    thanks again all

    ** if necessary, i can scan more pages **

    BTW the book is "Numerical Computation of Electric and Magnetic Fields" by Charles W Stelle
  9. newbie, When you say "the E field at a point would depend on....where the source is" it sounds like you think the source is located at a single point. That's not true here; the source is distributed over the entire volume.
  10. Yes the source is distributed. Thanks jdavel
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