 (where \(\mathbf{A}(\mathbf{r})\) is the magnetic vector potential at point \(\mathbf{r}\) of space). This approach has the advantage that since \(S(C)\) is gauge-invariant, it may readily be considered a physically real quantity. Moreover, the effects of electromagnetism in the field-free region may be attributed to the fact that \(S(C)\) is nonvanishing for certain closed curves C within that region. But it is significant that, unlike the magnetic field and its potential, \(S(C)\) is not defined at each point of space at each moment of time.