ESE 330 Exam
1. Fig. 1 depicts the cross section of an infinitely long circular cylindrical structure that
has a uniform free charge volume density ρo within the cylindrical radius a that
remains uniform in the presence of other material effects in this problem. ε = εο
within the region for r < a. The region from r = a to r = b is a dielectric with total
permittivity ε1. The region for r > b is free space.
Determine
r r
r
E , D,V, P, " PS , " P within each region of the problem.
!!
εο
b
a
ρο
Fig. 1.
ε1
2. Fig. 2 shows a spherical region of uniform free charge volume density ρο with radius
a, except for the small spherical region of radius b in which the charge density is
absent. The centers of these spherical regions are a distance c above a perfectly
conducting grounded conductor of infinite extent in the horizontal direction. Point P
is located a distance d from the center of the large spherical region along the
horizontal centerline through these spherical regions. Find the force on a point
charge Q located at point P. Assume all this is embedded in free space.
d
a
b
P
Q
ρo
c
e
Ground plane
Fig. 2
In Fig. 3, a dielectric material of permittivity ε sliding freely in a cylindrical capacitor
experiences a mechanical force Fe of electrical origin in the axial direction. Find an
expression for Fe in terms of the material and geometric parameters shown in the figure.
Note: The capacitance of a cylindrical capacitor with the same radii of length L’
uniformly filled with a dielectric is given by C = (2"#L' ) /ln(b /a) .
L
V=0
b
V=Vo
a
!
Fe
ε
x
Fig. 3
εo