Why does the V/Hz ratio of a motor affect the magnetic field strength?
Consider the equivalent circuit for one phase of an induction motor shown below. The current, \$Im\$ in the magnetizing inductance \$Xm\$ determines the stator magnetic field strength. For a simple approximation, we can assume that \$Xs = 0\$ and everything else in the circuit except \$Xm\$ is infinite. We can then say that \$Im = \frac{V}{Xm}\$ 

Since \$Xm = 2*Pi*f*Lm\$, we can say that $$Im = \frac{V}{f}*\frac{1}{(2*Pi*Lm)}$$.

If we include all of the other components in the analysis, we will see that they have some influence, but the simple approximation shows pretty well what is happening.


Diagram adapted from Malcom Barnes "Practical Variable Speed Drives and Power Electronics"