A new method is suggested for calculation of transient electric field response to conducting magnetically viscous earth excited by a grounded line source. Calculation algorithms are implemented in the computer program FwLL_MV. Using a uniform, conducting magnetically viscous half-space as an earth model, we have shown that magnetic relaxation affects the TEM response of equatorial and in-line arrays. As in the case of loop arrays, apparent resistivity steadily decreases with time. The higher the half-space resistivity and the shorter the offset, the earlier the voltage and the apparent resistivity begin to decrease as 1/t. Magnetic relaxation and decay of eddy currents are independent processes within the range of resistivities typical of rocks.