In the mathematical model of melting of a tungsten plate exposed to a pulsed electron beam, the calculation of the current distribution in the medium is added. The model takes into account the heterogeneity of the resistivity. This enables modeling of non-uniform heated material. The current is expected to spread into the depth due to the increased resistance of the heated part. Changing the thickness of the tungsten plate, one can increase the current density in the melt. The calculation results for parameters corresponding to those used on the BETA facility at BINP SB RAS show that no current concentration occur. The Ampere force is not large enough for the rotation observed in the experiments. © Published under licence by IOP Publishing Ltd.