LOCAL FIELD Meaning and
Definition
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The term "local field" refers to a concept primarily used in physics and mathematics to describe the strength and direction of an electromagnetic field at a specific point in space. The local field is a vector field that characterizes the behavior of electric and magnetic fields in the immediate vicinity of a given location. It is influenced by the presence of charged particles and nearby electromagnetic sources.
In physics, the local field is often represented by the vector sum of the field generated by the charges within the immediate vicinity. This can include the contribution from nearby sources, as well as the field generated by the charges themselves. The local field plays a crucial role in understanding the interaction between charged particles and their environment, providing insights into phenomena such as light scattering, polarization, and other electromagnetic interactions.
In mathematics, the concept of a local field can also refer to a field with a well-defined notion of distance and topology, typically associated with the study of number theory. Local fields often arise as completions of global fields, such as the real numbers or rational numbers, and provide a useful framework for investigating arithmetic properties, including local number theory and local algebraic geometry.
Overall, whether employed in physics or mathematics, the local field serves as a fundamental tool for analyzing the behavior and properties of electromagnetic fields and integers, respectively, in a specific region of interest.
Etymology of LOCAL FIELD
The word "local" originates from the late Middle English word "locale", which directly comes from the Latin word "localis", meaning "pertaining to a place". It is related to the Latin word "locus", meaning "place".
The word "field" in this context refers to a specific mathematical concept known as a field. The term "field" is derived from the Old English word "feld", which meant an open expanse of land. This word has Indo-European origins.
When combined, the term "local field" typically refers to a mathematical concept, mainly in algebraic number theory, rather than being strongly linked to a specific etymology.
