Static means simplifying Maxwell's equations such that there is no coupling at all between E and B fields:

ε div(E)= ρ

curl(B)=µ J

With quasi-static, one form of coupling between B and E is considered: the E field generates conventional current in conductive materials (Ohms Law) and then this conventional current adds to the external J stimulus and generates B in the normal (Biot-Savart) way.

curl(B)=µ(Jexternal+σE)

In both static and quasi-static, the time derivative terms in Maxwell's equations are set to zero. In other words, the displacement current term that Maxwell added to Ampere's Law is set back to zero and Faraday's Law becomes:

curl(E) = -dB/dt = 0

In contrast, full wave solvers consider all the time derivative coupling terms in Maxwell's equations to be finite.

Best regards,

-- Colin Warwick

High Speed Digital Blog