The research on the theory of arc in switchgear is the key problem in the field of power transmission equipment. We introduce a mathematical inverse method to reconstruct the arc shape and current density. The operator equation is established and discretized into algebraic equations according to the electromagnetic forward analysis. To overcome the ill posedness of the electromagnetic inverse problem

the real-coded quantum evolutionary algorithm based on allele（A-RQEA） along with the parallel processing of regularization theory is adopted. Both the arc position and the arc shape are reconstructed by the efficient and accurate intelligent optimization algorithm

with the current distribution inversed by means of truncated singular value decomposition（TSVD）. The L-curve criterion is used to select the regularization parameter. The results show that

by means of combining the nonlinear optimization with the regularization inversion

the arc shape and the current distribution can be reconstructed via magnetic field distribution accurately. The maximum relative error of the calculated current value for each arc current line by means of TSVD is 8%

and the minimum relative error is 0.03%

the inversed current density from the core and the edge regions is consistent with the trend of preset distribution

which will help understand the complex physical characteristics for the switching arc.