# Del Operator

by newbie101
Tags: operator
 P: 16 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 thanks newbie
 P: 618 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?
 Sci Advisor HW Helper PF Gold P: 12,016 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..
 P: 16 Del Operator 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 newbie101
Mentor
P: 11,594
 Quote by newbie101 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"
That means that, for example,

$$\nabla_f V = \frac {\partial V}{\partial x_f} \hat {\bold i} + \frac {\partial V}{\partial y_f} \hat {\bold j} + \frac {\partial V}{\partial z_f} \hat {\bold k}$$

whereas

$$\nabla_s V = \frac {\partial V}{\partial x_s} \hat {\bold i} + \frac {\partial V}{\partial y_s} \hat {\bold j} + \frac {\partial V}{\partial z_s} \hat {\bold k}$$

where V is some function of $x_f$, $y_f$, $z_f$, $x_s$, $y_s$, and $z_s$ (that is, depends on both the field coordinates and the source coordiates).
 P: 618 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?
 P: 16 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 newbie101 ** if necessary, i can scan more pages ** BTW the book is "Numerical Computation of Electric and Magnetic Fields" by Charles W Stelle
P: 618
 Quote by newbie101 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
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.
 P: 16 Yes the source is distributed. Thanks jdavel

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