Differences between Del Operators at Field/Source Points

In summary, the difference between the del operators is that del-f differentiates with respect to the field point, while del-s differentiates with respect to the source point.
  • #1
newbie101
16
0
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
 
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  • #2
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
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
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

HelmholtzPage1.jpg


HelmholtzPage2.jpg



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
 
Last edited:
  • #5
newbie101 said:
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,

[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
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
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, I am 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 wouldn't 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
newbie101 said:
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.
 
  • #9
Yes the source is distributed. Thanks jdavel
 

1. What is the difference between field and source points?

The main difference between field and source points is their location in space. Field points are points in space where the field is being measured, while source points are points where the field is being generated.

2. Why is it important to understand the differences between del operators at field/source points?

Understanding the differences between del operators at field and source points is important because it helps us to accurately analyze and describe electromagnetic fields. It also allows us to properly apply Maxwell's equations and solve problems related to electromagnetic fields.

3. How do the del operators differ at field and source points?

The del operator, also known as the gradient operator, is a vector operator that describes the spatial variation of a field. At field points, the del operator operates on the field itself, while at source points, it operates on the sources of the field, such as charges and currents.

4. Can the del operators be used interchangeably at field and source points?

No, the del operators cannot be used interchangeably at field and source points. They have different mathematical expressions and operate on different quantities at each type of point. Using the wrong del operator can lead to incorrect analysis and solutions.

5. What is the significance of the del operators in electromagnetic theory?

The del operators play a crucial role in electromagnetic theory as they are used to describe the behavior of electromagnetic fields. They help us to understand and analyze the properties of fields, such as electric and magnetic fields, and are essential in the development of many applications in electromagnetics, such as antennas and communication systems.

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