Exam II: Take Home Exam
Due on March 26, 2008 by 5:40 p.m.
20 points
1.
Two long, cylindrical conductors of radii a1 and a2 are parallel and separated by a
distance d which is large as compared to either a1 or a2.
(a)
Show that the capacitance per unit length of this configuration is
1
C 
d
  4 ln  , where a is the geometric mean of the two radii.
L 
a
Note: In the Gaussian units used in this problem Gauss’ Law is expressed as
 
 E  d s  4 Qencl .
In SI units you will be different than the above expression for C/L by a constant
that includes ε0.
(b)
Calculate the attractive force between the conductors if each conductor carried
equal and opposite charges (±Q).
2.
Apply the method of images to the problem of the potential inside a hollow,
grounded conducting sphere of inner radius a, with a point charge q placed inside
it. Set up the problem with an image charge q’ outside the sphere and find
(a)
The potential inside the sphere.
(b)
The induced surface charge density.