An infinitely long rod of radius R carries a uniform volume chargedensity 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).
(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.
(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).
(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).
Please explain your strategy and include any labels ordiagrams.
An infinitely long rod of radius R carries a uniform volume chargedensity 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).
(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.
(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).
(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).
Please explain your strategy and include any labels ordiagrams.
