### 4.5 Derived quantities, electric currents, and

The well-known large uncertainties in the horizontal magnetic field component, in particular in weak
field regions (see Section 4.1), cause large errors when computing the electric current density with finite
differences via Equation (13). Even more critical is the computation of with Equation (14) in weak
field regions and in particular along polarity inversion lines (see, e.g., Cuperman et al., 1991). The nonlinear
force-free coronal magnetic field extrapolation is a boundary value problem. As we will see later, some of
the NLFFF codes make use of Equation (14) to specify the boundary conditions while other
methods use the photospheric magnetic field vector more directly to extrapolate the field into the
corona.