This paper investigates the reason behind the low magnetic field computation in cylindrical coordinates using finite difference method, when boundary conditions of the third or fourth kind are used. The same field computation has also been performed using the finite element method but this problem did not occur. It thus, presents a technique to overcome the problem of low magnetic field calculation using finite difference method. The results obtained by the new technique are in close agreement with the finite element method as well as the analytical solution. Finally, an analysis of the possible source of error in modeling magnetostatic boundary conditions in finite difference formulation of vector Poisson or Laplace equation in cylindrical coordinates is performed.