Conservative Vector Fields and the Intersect Rule
DOI:
https://doi.org/10.58445/rars.372Keywords:
Multivariable Calculus, Vector Calculus, Vector Physics, Newtonian Mechanics, Vector Fields, Gradient FieldsAbstract
Conservative vector fields are defined as the gradient of a scalar-valued potential function. Gradient fields are irrotational, as in, the curl in all conservative vector fields is zero. Additionally, line integrals in conservative vector fields are path independent, and line integrals over closed paths are always equal to zero. Gradient fields represent conservative forces, and the associated potential function is analogous to potential energy associated with said conservative forces. The Intersect Rule provides a new, unique shortcut for determining if a vector field is conservative and deriving potential functions, by treating the indefinite integral as a set.
References
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