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We derive an exact expression for the differential conductance for a quantumdot in an arbitrary magnetic field for small bias voltage. The derivation isbased on the symmetric Anderson model using renormalized perturbation theoryand is valid for all values of the on-site interaction $U$ including the Kondoregime. We calculate the critical magnetic field for the splitting of the Kondoresonance to be seen in the differential conductivity as function of biasvoltage. Our calculations for small field show that the peak position of thecomponent resonances in the differential conductance are reduced substantiallyfrom estimates using the equilibrium Green's function. We conclude that it isimportant to take the voltage dependence of the local retarded Green's functioninto account in interpreting experimental resultsComment: 8 pages, 4 figures; Replaced by a fully revised version with minor  corrections in the tex

Non-equilibrium differential conductance through a quantum dot in a magnetic field