[SOLVED] Physics 311 Homework Set 5

1. Find the electric field a distance s from an infinitely long straight wire, which carries a
uniform line charge .2. Find the electric field inside a sphere which carries a charge density of the form
(r) = kr (1)
for some constant k. Hint: This charge density is not uniform, and you must integrate to
get the enclosed charge.3. A hollow spherical shell carries charge density
(r) = kr (2)
for some constant k in the region a r b (Fig. 2.25).Find the electric field in the three regions:
a) r<a.
b) a<r<b.
c) r>b.4. A long coaxial cable (Fig. 2.26) carries a volume charge density
(s) = 0
s
a (3)
on the inner cylinder (radius a), and a uniform surface charge density on the outer
cylindrical shell (radius b).This surface charge is negative and of just the right magnitude
so that the cable as a whole is electrically neutral.Find the electric field in each of the three regions
a) s<a.
b) a<s<b.
c) outside the cable (s>b).
d) Plot |E~ | as a function of s.5. One of these is an impossible electrostatic field. Which one?
a) E~ = k [x2y x + 3yz2 y + 2xz3 z]
b) E~ = k [3y2 x + (6xy + 3z2) y + 6yz z].Here k is a constant with the appropriate units. For the possible one, find the potential,
using the origin as your reference point. Check your answer by computing r~ V .[Hint: You must select a specific path to integrate along. It doesnt matter what path you
choose, since the answer is path-independent, but you simply cannot integrate unless you
have a particular path in mind.]