Question

In Thomson's experiments with electron beams, when the magnetic force FM balanced the force of the electric field Fe, the velocity of the beam was given by the ratio--- divided by--- .

Answer 1

In Thomson's experiment, when the magnetic force balanced the electric force, the velocity of the beam was
$v= \frac{E}{B}$
where E is the magnitude of the electric field and B the magnitude of the magnetic field.

Let's see why. The force exerted by the electric field of intensity E on each electron is
$F=eE$
where $e$ is the electron charge.
The force exerted by the magnetic field of intensity B on each electron is
$F=evB$
where v is the speed of the electrons. 

When the two forces are balanced, we have:
$eE=evB$
from which we find
$v= \frac{E}{B}$