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In connection with the Casimir effect for a spinor field in presence ofexternal magnetic field, of special interest are solutions of the Diracequation in the domains restricted by two planes, which have vanishing thethird projection of the conserved current J^{z} on two boundaries. Generalconditions for vanishing the current are formulated, they reduce to linearhomogeneous algebraic system, for which solutions exist only when vanishing thedeterminant of the linear system, that is for the roots of a 4-th orderalgebraic equation with respect to the variable e^{2ik a}, where a is ahalf-distance between the planes, and k stands for the third projection of theDirac particle momentum. All solutions of the equation have been foundexplicitly, each of them provides us in principle with a special possibility toget the quantization rules for parameter k; the most of produced expression forthe roots can be solved with respect to parameter k only numerically.Generally, solutions e^{2ik a} depend on 4 arbitrary phase parameters whichinfluence the appropriate wave functions with vanishing current:J^{z}(z=-z,+a)=0.

General conditions for vanishing the current J^{z} for Dirac field on boundaries of the domain between two planes