Register to reply 
Del Operatorby newbie101
Tags: operator 
Share this thread: 
#1
Apr2005, 05:33 AM

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 


#2
Apr2005, 09:05 AM

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? 


#3
Apr2005, 10:32 AM

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.. 


#4
Apr2005, 12:22 PM

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 (A2) through (A5), the operator 'delf' differentiates with respect to field point rf, while the operator 'dels' differentiates with repect to the source point rs" May I know the difference between the operators here. Page 2 bottom half " From Equation (A1) since F(rs) is a function of the source point alone, but "delf" 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 


#5
Apr2005, 02:01 PM

Mentor
P: 11,749

[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] whereas [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). 


#6
Apr2005, 02:22 PM

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? 


#7
Apr2005, 02:47 PM

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 


#8
Apr2005, 03:15 PM

P: 618




#9
Apr2005, 09:59 PM

P: 16

Yes the source is distributed. Thanks jdavel



Register to reply 
Related Discussions  
Del operator?  Calculus  5  
Adjoint of an operator  Linear & Abstract Algebra  8  
Operator O?  General Math  11  
I'm looking at this question:'If we assume as oscillation of form  Introductory Physics Homework  3  
Help with this operator  General Math  2 