In the context of vector fields and potential functions, which of the following statements best explains the relationship between a scalar function, its gradient, and the resulting vector field?
A) The gradient of a scalar function forms a vector field, and if the vector field is conservative (zero curl), the scalar function is called the potential function of the vector field.
B) The gradient of a vector function forms a scalar field, and if the scalar field is conservative (zero divergence), the vector function is called the potential function of the scalar field.
C) The curl of a scalar function forms a vector field, and if the vector field is conservative (zero divergence), the scalar function is called the potential function of the vector field.
D) The curl of a vector function forms a scalar field, and if the scalar field is conservative (zero curl), the vector function is called the potential function of the scalar field.
