Question #3 In order to create a neutralizer filament for the ion engine of Question #3, we will use the principle of thermionic emission, which involves heating a metal to "boil off" electrons from its surface. These filaments are lengths of wire that are heated resistively in order to release the electrons. To find the electron current density of a specific metal at certam temperatures, we need to use the Richardson Equation. J - AT' exp(-ed / KI) (Richardson Equation) where A_ 7(10: ) A- 9 -4.552V, k_ 138(10-9) J/K 1) Using the above expression, create a plot of emitted current per unit length ve. temperature for a 20 AWG wire (diameter = 0.8118 mm). 2) Given the resistivity of Tungsten and using the data from above, design a filament to provide 750 mA of electron current with 20 AWG and find the current through the filament. Assume each filament needs to have a length of 7 cm and all the power through the filament is radiated away (via black body radiation). Emissivity of Tungsten: /= 0.15 Resistivity of Tungsten: p - 2(10-10)7: + 3(10-10)7- 3(10-") 0-m ([T ]- K)