An electrostatic dust precipitator that is installed in a factory smokestack includes a straight metal wire of length L = 0.8 m
that is charged approximately uniformly with a total charge Q = 0.4 × 10−7 C. A speck of coal dust (which is mostly
carbon) is near the wire, far from both ends of the wire; the distance from the wire to the speck is d = 1.5 cm. Carbon has
an atomic mass of 12 (6 protons and 6 neutrons in the nucleus). A careful measurement of the polarizability of a carbon
atom gives the value
(a) Calculate the initial acceleration of the speck of coal dust, neglecting gravity. Explain your steps clearly. Your
answer must be expressed in terms of Q, L, d, and α. You can use other quantities in your calculations, but your
final result must not include them. Don't put numbers into your calculation until the very end, but then show the
numerical calculation that you carry out on your calculator.
(b) If the speck of coal dust were initially twice as far from the charged wire, how much smaller would the initial
acceleration of the speck be?