In 1897, J. J. Thomson "discovered" the electron by measuring the charge-to-mass ratio of "cathode rays" (actually, streams of electrons, with charge
(a) First he passed the beam through uniform crossed electric and magnetic fields
(b) Then he turned off the electric field, and measured the radius of curvature,
We want zero deflection. That means zero force:
We can cancel the factor of
With magnitudes
So
We can use the already studied cyclotron motion (see Example 5.1). Circular uniform motion is sustained when
We can solve for the ratio