It is not possible to see very small objects, such as viruses,
using an ordinary light microscope. An electron microscope can view
such objects using an electron beam instead of a light beam.
Electron microscopy has proved invaluable for investigations of
viruses, cell membranes and subcellular structures, bacterial
surfaces, visual receptors, chloroplasts, and the contractile
properties of muscles. The "lenses" of an electron microscope
consist of electric and magnetic fields that control the electron
beam.
As an example of the manipulation of an electron beam, consider an
electron traveling away from the origin along the x axis
in the xy plane with initial velocity
vî =
viî. As it passes through the
region x = 0 to x = d, the electron
experiences acceleration a =
axî +
ayĵ, where
ax and ay are constants.
For the case vi = 1.78 ✕ 107 m/s,
ax = 8.28 ✕ 1014 m/s2,
and ay = 1.66 ✕ 1015
m/s2, determine the following, at x =
d = 0.0100 m.
(a) the position of the electron
yf = m
(b) the velocity of the electron
vf = m/s
î + m/s ĵ
(c) the speed of the electron
|vf| = m/s
(d) the direction of travel of the electron (i.e. the angle between
its velocity and the x axis)
θ = °
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