Recall the problem from our last homework where you calculated the particle flux through a surface in a plasma. you did it by calculating the flux going one way at a time. if you know the flux of particles, and you know the charge per particle, then you also know the flux of charge, i. e. the current density for electrons je or ions 7.. now, consider a space ship flying through a low-density space plasma. it is being piloted by everyone's favorite space dog, laika (look her up). laika knows that the outside of her ship is being charged up over time and gaining a non-zero potential, and she needs you to tell her if she should be worried about it the plasma is an electrically neutral hydrogen plasma in thermal equilibrium (i. e. same temp. for ions and electrons) with temperature kt 0.01 ev. eventually, the electron and ion current density into the sides of the ship reach equilibrium ji and the ship's potential φ stops changing. what is the ship's potential at equilibrium, and is it large enough in magnitude that laika should be worried? consider the sides of laika's ship to be very wide conducting plates hint: the number density term from the flux calculation is really the local density at the surface where the flux is calculated. recall the form of the number density as a function of position for a conducting plate in a plasma from lecture, and think about what position you care about here