When should a sincere man stop pursuing a girl?

For those that have the seventh printing of Goldstein's "Classical Mechanics" so I don't have to write any equations here. The Lagrangian for electromagnetic fields (expressed in terms of scalar and vector potentials) for a given charge density and current density that creates the fields is the spatial volume integral of the Lagrangian density listed in Goldstein's book as Eq. (11-65) (page 366 in my edition of the book). Goldstein then considers the case (page 369 in my edition of the book) in which the charges and currents are carried by point charges. The charge density (for example) is taken to be a Dirac delta function of the spatial coordinates. This is utilized in the evaluation of one of the integrals used to construct the Lagrangian. This integral is the spatial volume integral of charge density multiplied by the scalar potential. What is giving me trouble is as follows.

In the discussion below, a "particle" refers to an object that is small in some sense but has a greater-than-zero size. It becomes a point as a limiting case as the size shrinks to zero. In order for the charge density of a particle, regardless of how small the particle is, to be represented by a delta function in the volume integral of charge density multiplied by potential, it is necessary for the potential to be nearly constant over distances equal to the particle size. This is true (when the particle is sufficiently small) for external potentials evaluated at the location of the particle of interest, where the external potential as seen by the particle of interest is defined to be the potential created by all particles except the particle of interest. However, total potential, which includes the potential created by the particle of interest, is not slowly varying over the dimensions of the particle of interest regardless of how small the particle is. The charge density cannot be represented by a delta function in the integral of charge density times potential, when the potential is total potential, regardless of how small the particle is. If we imagine the particles to be charged marbles (greater than zero size and having finite charge densities) the potential that should be multiplying the charge density in the integral is total potential. As the marble size shrinks to zero the potential is still total potential and the marble charge density cannot be represented by a delta function. Yet textbooks do use this representation, as if the potential is external potential instead of total potential. How do we justify replacing total potential with external potential in this integral?

I won't be surprised if the answers get into the issues of self forces (the forces producing the recoil of a particle from its own emitted electromagnetic radiation). I am happy with using the simple textbook approach and ignoring self forces if some justification can be given for replacing total potential with external potential. But without that justification being given, I don't see how the textbooks reach the conclusions they reach with or without self forces being ignored.

Hello

I would be appreciated if you could guide me on how to integrate the product of an arbitrary function and Dirac delta function as attached?

Please what is your opinion according your experience?

Hi dear colleagues,

What is the main secret for the success of any conjugal relationship?

For me, love, understanding and consensus (compatibility) in thoughts (ideas) is the key secret.

Thanks for sharing ur experiences with us,

Kind regards

Which is best, Love marriage or arrange marriage?

Human being is a social being that needs love and appreciation as well as matter and is an essential part of its continuation

Sacrament or Samskar means purification, Hindu have sixteen samskaras from Pre-birth to death. Marriage sacrament or Vivaha samskar is one of the sixteen samskaras.

I observed that most people enjoy courtship because love is active during this period. But in marriage, there seems to be conflicts because here love is passive. I discovered that most marriages collapse because men are pretenders in courtship period. Most of them are no more who they used to be during courtship- a romantic period. They grow traditional and more authoritative whereas women want to be romantic forever. Men should not tolerate in courtship what they cannot tolerate in marriage- a classical period. My understanding of Romantic Period and Classical Period is that of Courtship Period and Marital Period.

I am looking for articles related to love marriage among girls, especially in Bangladesh and South Asian perspectives. Any suggestions, please.