  We show that non-frustrated and frustrated ladders in a magnetic field can be
systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic
field in the limit where the rung coupling is the dominant one. This mapping is
valid in the critical region where the magnetization goes from zero to
saturation. It allows one to relate the properties of the critical phase
($H_c^1$, $H_c^2$, the critical exponents) to the exchange integrals and
provide quantitative estimates of the frustration needed to create a plateau at
half the saturation value for different models of frustration.
