Amuch studied system in condensed matter physics is the so-called "dusty plasma". it is a mixture of electrons, ions, and small dust particles with radii on the order of a few microns. as the dust particles move through the plasma, they collect a net negative charge, due to the increased mobility of electrons as compared to the positive ions. as the negative charge increases in magnitude, positive ions in the plasma are attracted to the dust particles, inducing a shielding effect. this shielding effect produces a potential with the form v(r)= ae−λr r where a and λ are constants. this is called the yukawa potential (or the screened coulomb potential). find a) the electric field e(r) b) the charge density rho(r) c) the total charge q.