Over the past decades, there has been significant controversy regarding the role of exogenous electromagnetic (EM) fields on the dynamics of molecules in living cells. Here we present a model of electromagnetic forces in the synaptic cleft using the bidomain theory as a framework and the averaged field theory as the theoretical basis, suggesting that the exogenously induced magnetic field may modify the neurotransmitter dynamics. Our model is based on a voltage cell membrane amplification due to the Hall effect principle and the hypothesis that synaptic cleft electric conductivity is represented by tensors with non-zero off-diagonal terms. The physical interpretation of the off-diagonal components is explained, and analytical expressions for the induced magnetic field and conductivity tensor are derived.