  We derive an exact expression for the differential conductance for a quantum
dot in an arbitrary magnetic field for small bias voltage. The derivation is
based on the symmetric Anderson model using renormalized perturbation theory
and is valid for all values of the on-site interaction $U$ including the Kondo
regime. We calculate the critical magnetic field for the splitting of the Kondo
resonance to be seen in the differential conductivity as function of bias
voltage. Our calculations for small field show that the peak position of the
component resonances in the differential conductance are reduced substantially
from estimates using the equilibrium Green's function. We conclude that it is
important to take the voltage dependence of the local retarded Green's function
into account in interpreting experimental results
