a) Give a statement of Gauss' Law in its integral form.
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Transcribed Image Text:Q1 a)
Give a statement of Gauss' Law in its integral form.
b)
Laplace's equation may be expressed in the cylindrical coordinate
system for a structure exhibiting radial symmetry as follows:
1 a
r ər
= 0
It can also be shown that the electric field about a line charge inside
a dielectric is given by:
E = -V$ =
A coaxial cable has an inner conductor radius a and an outer radius
b. The outer conductor is connected to earth, and the inner raised to
a potential V.
(i)
Show that the radial potential distribution inside the dielectric
is described by:
-In
2πε, εο
From this, derive an expression for the Capacitance per unit
p(r)
length of the cable
c)
A coaxial cable has the following specifications:
a = 1.0mm, b = 3.2mm, spacer &r = 2.1
The outer conductor is earthed and has thickness 0.2mm. The inner
conductor is raised to a potential of 1kV, and balanced opposing
charges allowed to accumulate on the conductor surfaces.
(i) Show that the charge per unit length deposited on each
conductor is approximately 100nC m1
(ii) Calculate the magnitude of the electric field E| at radial
positions 0.5mm, 1.0mm, 2mm, 3.2mm and 5mm from the
midpoint.
(iii) Sketch plots of |E|(r) and $(r) with increasing radial distance
from the cable axis.
(iv) The dielectric strength of the spacer is 20kV/mm. Calculate the
maximum operating voltage of the cable, allowing for a safety
margin of 5:1
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