PROBLEMS TO BE WRITTEN UP AND TURNED IN AT RECITATION
This problem is due at your first recitation meeting after WED 9/29.
The problem should be written on a single sheet of paper (front and back),
or if multiple sheets are used, staple them together. For full credit,
the work must be neat, with clearly labeled diagrams. The labels must
be in BOTH words and symbols. For each part of each problem, you must
BRIEFLY explain your strategy in words, as well as neatly showing your
physics equations and math, with proper units.
E2. An infinitely long rod of radius R carries a uniform
volume charge density rho (rho > 0).
(a) Show how to use Gauss' Law to prove that the
electric field inside this rod points radially
outward and has magnitude
E = (rho*r)/(2*epsilon_0). (10 points)
(b) Find the potential difference between a initial
radial position r_i and a final radial position
r_f; i.e. find an expression for the potential
at r_i subtracted from the potential at r_f.
(16 points)
(c) Choose potential equal zero at the central axis
of the rod and find the potential as a function
of r inside the rod (i.e. for r < R). Make a
graph of your resulting potential function (plot
V versus r). (7 points)
(d) Instead of the case in (c), choose potential equal
zero at the surface of the rod (i.e. at r=R) and
find the potential as a function of r inside the
rod (i.e. for r < R). Again make a graph of your
resulting potential function (plot V versus r).
(7 points)