The resistivity of a semiconductor can be modified by adding different amounts
of impurities. A rod of semiconducting material of length and cross-
sectional area A lies along the -axis between 0 and . The
material obeys Ohm's law, and its resistivity varies along the rod according
to exp(). The end of the rod at 0 is at a
potential greater than the end at . (a) Find the total resistance
of the rod and the current in the rod. (b) Find the electric-field magnitude
in the rod as a function of . (c) Find the electric potential
in the rod as a function of . (d) Graph the functions , ,
and for values of between 0 and .