Potential Function

Being dependent on the property of conservation of vector fields if the following properties are true for a field $F$

• it is a conservative field
• it is the gradient field of some scalar function $f$ such that $F=\nabla f$ then $f$ is called a potential function of $F$. → An electric potential is a scalar function whose gradient field is a electric field.

If such a potential function $f$ has been found to be the potential of $F$ the following statement holds

$$\int \_A^{B}F\cdot dr=\int \_A^B\nabla f\cdot dr=f(B)-f(A)$$

optimizing the evaluation of line integrals over any path from $A$ to $B$.