¿Por qué para determinar el rotacional de un campo vectorial se requiere de una función potencial?

En cálculo vectorial, un potencial vectorial es un campo vectorial cuyo rotacional es un campo vectorial. Esto es análogo al potencial escalar, que es un campo escalar cuyo gradiente negativo es también un campo vectorial.
Formalmente, dando un campo vectorial v, un potencial vectorial es un campo vectorial A tal que
V=∇*A
Si un campo vectorial v admite un potencial vectorial A, entonces de la igualdad ∇*(∇*A)=0
la divergencia del rotacional es cero se tiene ∇*V=∇*(∇*A)=0 lo cual implica que v debe ser un campo vectorial solenoidal.
El potencial vectorial dado por un campo solenoidal no es único. Si A es un vector potencial para v, entonces también
A+∇m donde m es cualquier función escalar diferenciable. Esto se sigue del hecho de que el rotacional del gradiente es cero.
La no unicidad lleva a un grado de libertad en la formulación de la electrodinámica, o norma libre, y requiere elegir una norma.


(((In vector calculus, a vector potential is a vector field whose curl is a vector field. This is analogous to the scalar potential, a scalar field whose negative gradient is also a vector field.
Formally, given a vector field v, a vector potential A is a vector field such that
V = ∇ * A
If a vector field v admits a vector potential A, then the equality ∇ * (∇ * A) = 0
the divergence of the curl is zero we have ∇ * ∇ * V = (∇ * A) = 0 which implies that v must be a solenoidal vector field.
The vector potential given by a solenoidal field is not unique. If A is a potential vector for v, then also
A + ∇ m where m is any differentiable scalar function. This follows from the fact that the curl of the gradient is zero.
The non-uniqueness leads to a degree of freedom in the formulation of electrodynamics, or standard free, and requires choosing a standard.)))

clear the potential is a vector field by determining some aspect as a free rule in a way that a vector potential cimultanea establese which acid determined by this function given by the cula a solenoidal field is not unique.

the curl of a vector field always requires a potential function as the equation satisfied by the potential function, ie if the gradient of f is equal to f is a function f estonces eg the voltage potential is a function Electics field potential and static poe that the volataje sometimes called potential.