5.
Charge and mass
J.J.
Thomson had found the velocity of the cathode rays,
but needed to know their specific charge. The specific
charge of an object is its charge divided by its mass.
By
turning off the magnetic field, Thomson could measure
the deflection of the cathode rays in the electric field
alone.
This
deflection is due to the cathode rays acquiring velocity
in a direction parallel to the electric field. The velocity
of the particles perpendicular to the field remains
constant.
This
new velocity parallel to the field equals the acceleration
in the field divided by the time in the field. The equations
used to relate this to the deflection angle are shown
in the diagram above.
The
field strength (E), distance over which it
acted (d), and angle (θ) are measurable,
and Thomson had already calculated the ray's velocity
(v). Therefore by measuring the deflection
Thomson could calculate the specific charge (q/m).
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