 An additional term Ps was first added into D by Wang in 2017, where Ps is "the polarization created by the electrostatic surface charges owing to mechanical triggering, different from the electric field induced medium polarization P. The D" can be rewritten as formula_10, so the displacement current density is obtained by

formula_11 (2.2)

Then the Maxwell's equations can be expanded as

formula_12 (3.1)

formula_2 (3.2)

formula_3 (3.3)
formula_15 (3.4)

These equations are the cornerstones for deriving the output characteristics of nanogenerators, from which the output current and voltage, and the related electromagnetic radiation of a nanogenerator have all been derived.The polarization Ps created by the electrostatic surface charges can be expressed by the following equation, when defining the charge density function "σs"(r,"t") on the media surface by a shape function of "f"(r,"t")=0.formula_16 (4)

where the delta function "δ"("f"(r,"t")) is introduced to confine the media shape.