Answer Happy

In an industrial application, two very large parallel metal plates have constant electric potentials, o V (at z = 0) and 40 V (at z = L). A gas of relative permittivity ε fills the space between the metal plates. A special device is used to generate slowly moving protons between the plates with a volume charge density p = po sin where po has a constant value. Effects caused by the motion of the protons may be ignored. The plates are very large so edge effects can also be ignored. a) Show that the electric displacement field between the plates is L D= -Po - cos s63 +C1 where C1 is an integration constant. b) Use the expression for Din part a) to obtain an expression for the electric field between the plates. c) Use your answer to part b) to obtain an expression of the electrostatic potential field between the plates. Determine any integration constants that may be in the expression. d) Use the expression for Din part a) and your answer to part b) to show that the volume polarization charge density between the plates is (E - 1) TZ Pp = -Po sin E e) Determine the expression for the surface polarization charge density at z = 0.