  The effect of a magnetic field on the spectral density of a $\rm{S=1/2}$
Kondo impurity is investigated at zero and finite temperatures by using
Wilson's numerical renormalization group method. A splitting of the total
spectral density is found for fields larger than a critical value
$H_{c}(T=0)\approx 0.5 T_{K}$, where $T_{K}$ is the Kondo scale. The splitting
correlates with a peak in the magnetoresistivity of dilute magnetic alloys
which we calculate and compare with the experiments on
$\rm{Ce_{x}La_{1-x}Al_{2}}, x=0.0063$. The linear magnetoconductance of quantum
dots exhibiting the Kondo effect is also calculated.
