Confussion about Del operator for field point vs source point.

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SUMMARY

The discussion centers on the confusion surrounding the use of the Del operator (\nabla) in electrodynamics, specifically regarding its application to field points versus source points. The Del operator serves as a spatial derivative for both scalar and vector fields, which are inherently spatially dependent. The distinction between \nabla acting on the field point and \nabla' acting on the source point is clarified through the example of the gradient of a scalar function V and the divergence of a vector field E, both of which vary at different spatial locations.

PREREQUISITES
  • Understanding of multi-variable calculus
  • Familiarity with electrodynamics concepts
  • Knowledge of scalar and vector fields
  • Basic comprehension of the Del operator and its applications
NEXT STEPS
  • Study the mathematical properties of the Del operator in vector calculus
  • Explore the differences between field points and source points in electrodynamics
  • Learn about the gradient and divergence in the context of electromagnetic fields
  • Investigate the role of integrals in electrodynamics, particularly in relation to potential functions
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Students and professionals in physics, particularly those specializing in electrodynamics, as well as mathematicians interested in vector calculus and its applications in physical theories.

yungman
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I electrodynamics, I've seen [itex]\nabla '[/itex] and [itex]\nabla[/itex] where first is spatial derivative respect to source point and later spatial derivative respect to field point.

I am confuse. According to multi-variables calculus, the [itex]\nabla[/itex] operator is spatial derivative of either a scalar or a vector field. Both of which are point form...which is absolutely spatial dependent only. I don't see what is the meaning respect to source or field points.

For example:

[itex]\nabla V[/itex] is the gradient of a scalar function V, and it has a different value at each individual point specified. So is [itex]\nabla \cdot \vec E[/itex] which is the divergence at a point in the space. These are regardless of whether it is a field or a source point.

I am confused. Please explain to me.

Thanks

Alan
 
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The integrand in the integral for phi is a function f(r,r') of two variables, r and r'.
Del acts on r, and Del' acts on r'.
 
Thanks

Alan
 

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