Coaxial Conductor System with Uniform Space Charge: A static space-charge distribution fills the region between two long coaxial conductors as shown. The center conductor is held at a potential of Vo with respect to the outer conductor, which is at ground potential. The charge density in the region between the conductors is uniform, given by p(r) Po. Find the field and potential inside by a V direct integration of Poisson's equation with appropriate boundary conditions. Once the potential + is found, find the total induced charge on each conductor. At what critical voltage does the charge on the anode go to zero? Note: the r in this problem is interpreted as the radial distance from the z-axis as in cylindrical coordinates. ++ ++. XX + xx xx xx x xxxx xx ++ + +++ +
Coaxial Conductor System with Uniform Space Charge: A static space-charge distribution fills the region between two long coaxial conductors as shown. The center conductor is held at a potential of Vo with respect to the outer conductor, which is at ground potential. The charge density in the region between the conductors is uniform, given by p(r) Po. Find the field and potential inside by a V direct integration of Poisson's equation with appropriate boundary conditions. Once the potential + is found, find the total induced charge on each conductor. At what critical voltage does the charge on the anode go to zero? Note: the r in this problem is interpreted as the radial distance from the z-axis as in cylindrical coordinates. ++ ++. XX + xx xx xx x xxxx xx ++ + +++ +
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Transcribed Image Text:Coaxial Conductor System with Uniform Space
Charge: A static space-charge distribution fills the
region between two long coaxial conductors as
shown. The center conductor is held at a potential
of Vo with respect to the outer conductor, which is
at ground potential. The charge density in the region
between the conductors is uniform, given by
p(r) = P₁ . Find the field and potential inside by a V
direct integration of Poisson's equation with
appropriate boundary conditions. Once the potential.
+
I
is found, find the total induced charge on each conductor. At what critical voltage does
the charge on the anode go to zero? Note: the r in this problem is interpreted as the
radial distance from the z-axis as in cylindrical coordinates.
+
x
xx
b
+
+++
X
хх
++
+++
+
++
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