If a

vector function **A** satisfies

**curl A** = 0

then you can define a

scalar potential function V such that

**grad** V =

**A**
this makes things much easier to deal with, since you now have a (1-component) scalar function instead of an (arbitrarily-large-number-of-components) vector function. You lose accuracy to the degree of an arbitrary additive

constant, but that can be solved with the

magic of

boundary value problems.

A popular use of the potential function in

physics is the

electric potential, which is the potential function of the

electric field in magnetostatic problems. In problems where the

magnetic field is non-static, the potential formulation becomes more complicated.