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Use vector signs clearly for vector quantities.
Write the unit of all evaluated quantities.
1) An infinitely long uniform line charge of density  L (C/m) is concentric with a
dielectric material of relative permittivity  r defined for a<r<b. r<a is free space.
Find:
a) The electric flux density in all regions,
b) The electric field intensity in all regions,
c) The polarization vector P in all regions,
d) The electrostatic potential difference between points A and B.
e) The equivalent polarization surface and volume charge densities.
f) Show that the total bound charge is zero.
L
r
b
0
a
A
B
2 ) a)
Prove that the Poisson’s equation in a charged region is  2V  

and write

down the Laplace’s equation.
b)Two infinite insulated conducting plates maintained at potentials 0 and V0 Volts are
placed at   0 and   0 planes respectively. Assuming that the region at r=0 is
excluded, determine:
i) The electrostatic potential distribution,
ii) The electric field intensity vector,
for the region 0    0 .
V0
V
ts
vol
  0
  0, V  0
3) There is a line (filamentary) current of I1 on the x-axis, a line current of I 2 on the yaxis and a curent sheet of J  J s0 aˆ z at y=4. What is the magnetic field H at P(2,2,2)?
y
I2
Current sheet
y=4
(2,2,2)
I1
x
4) N turns of wire are tightly wound on a toroidal frame of a rectangular cross section with
dimensions as shown. Assuming that the permeability of a medium for a<r<b is 1 (medium1)
and for b<r<c is  2 (medium 2), find:
a) The magnetic field intensity in both media,
b) The magnetic flux density in both media,
c) The total magnetic flux in the toroid,
d) The inductance of the system,
e) The magnetic energy stored by the system.
N turns
II
2 1
1 2
a
b
c
h