Week 6: Moving Charges and Magnetic Force 203
E field (down)
B field (in)
Collimating slits
v
q
Figure 66: A region of crossed fields functions as a velocity selector; only particles with just the
right velocity pass through undeflected.
down. The net force on the particle iszerowhen:
FB=qvB=qE=FE (416)
or when the particle happens to have the velocity
v=
E
B (417)
in thex-direction. In this case the particle travels through undeflected and exits through the
collimating slit on the right.
Particles that are travelling toofast, however, have a magnetic force that exceeds the electric
force and are deflectedup. They strike the barrier at the far end and fail to pass through the slit.
Similarly particles that are travelling too slowly have an electric force that exceeds the magnetic
force. They are deflecteddownand fail to make it through the second slit.
Note well that this is avelocityselector and passes all particles with the right velocityregardless
of their mass or their nonzero charge!The particle can have any charge, positive or negative (except
zero), or any mass – as long as it has the rightvelocityit will still make it through undeflected. This
makes it very useful for preparing particle beams for certain kindsof experiments. It is alsovery
closely relatedto theHall Effectdescribed later.
Example 6.2.5: Thomson’s Apparatus for measuringe/m
+ "pudding"
− "plums"
vs
− − − electron cloud
−
−
−
−
−
−
−
−
−
−
+ nucleus
+
Figure 67: The “plum pudding model” that prevailed in 1897 on left, along with a more accurate
representation of the current atomic model – a massive nucleus surrounded by a quantum “pudding”
(the electron cloud).
The year is 1897. People know that matter is made up of atoms, thatatoms are made up of
positive and negative charge, but the human speciesstill does not knowif the positive and negative
