[SOLVED] Physics 311 Homework Set 6

1. A hollow spherical shell carries charge density
(r) = kr (1)
for some constant k in the region a r b (Fig. 2.25). In Homework Set 5, you considered
this charge density and computed the electric field in the three regions. Using this electric
field in the three regions, calculate the potential at the center, using infinity as your
reference point.2. A long coaxial cable (Fig. 2.26) carries a volume charge density
(s) = 0
s
a (2)
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 potential dierence between a point on the axis and a point on the outer cylinder.
Note that it is not necessary to commit yourself to a particular reference point if you use
Eq. 2.22.3. Using Eqs. 2.27 and 2.30, find the potential at a distance z above the center of the charge
distributions in Fig. 2.34. In each case, compute E~ = r~ V .4. Find the potential on the axis of a uniformly charged solid cylinder, a distance z from the
center. The length of the cylinder is L, its radius is R, and the charge density is .
Use your result to calculate the electric field at this point.5. Consider four point charges located at the corners of a square with charges and coordinates
q1 = q @ x = y = 0 , q2 = 2q @ x = ` , y = 0
q3 = q @ x = y = ` , q4 = 3q @ x = 0 , y = ` (3)a) How much work did it take to bring in charge q1 from infinity and place it in its
corner?
b) How much work does it take to assemble the whole configuration of four charges?6. Find the energy stored in a uniformly charged sphere of radius R and charge q.
Do it three ways:
a) Use Eq. 2.43.
b) Use Eq. 2.45. Dont forget to integrate over all space.
c) Use Eq. 2.44. Take a spherical volume of radius a. What happens as a ! 1?