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 vi hat bold = vii hat bold. As it passes through the region x = 0 to x = d, the electron experiences acceleration a = axi hat bold + ayj hat bold, where ax and ay are constants. For the case vi = 1.90 ? 107 m/s, ax = 8.57 ? 1014 m/s2, and ay = 1.47 ? 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 i hat bold + m/s j hat bold
(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)
? =