Question

3. Dielectric breakdown of a gas (a) An electron starts from rest and moves a distance under the influence of a unifornm electric field of magnitude E. Assume that the displacement is in the direction of the electric field. What is the final kinetic energy of the electron? Give your answer in terms of q - charge of the electron, m-mass of the electron. E and (b) Suppose the final kinetic energy of the electron is 10 eV and 1 = 1.0 10-6 m. Determine E in V/m. Possibly useful data: q =-1.6 × 10-19 C, m = 9.1 × 10-31 kg. (c)* Air is primarily composed of neutral N2 and O2 molecules and is an insulator. There are always some free electrons in air (created if nothing else by radioactivity and cosmic rays) but their concentration is too low to make air significantly conducting. Free electrons move a typical distance l between collisions with air molecules; l is called the mean free path of the electrons. If an intense electric field is present (e.g. due to a thundercloud; see problem 8 of homework 2) the electron will be accelerated between collisions. If electrons are accelerated sufficiently, their collision will knock additional electrons out of the molecules as well as excite the molecules, causing them to subsequently relax by giving off light. If each collision yields several electrons, a chain reaction is established whereby each newly liberated electron undergoes further collisions liberating additional electrons. Under these conditions the air undergoes "dielectric breakdown": it gives off light and becomes conducting. Lightning bolts are conducting channels created by dielectric breakdown of air by the intense electric fields of thunderclouds. In fluorescent lights a low density gas (with a correspondingly long mean free path l) undergoes dielectric breakdown under comparatively weaker electric fields.

Answer 1