Homework Help: Potential of coaxial with two dielectrics?

1. Dec 30, 2014

lam58

The question asks to find the potential of the ungrounded outer conducting sheath of a coaxial cable when the inner conductor has a voltage of $$\frac{220}{\sqrt{3}} kV$$.

Coaxial conditions:
i) Central copper conductor of diameter 4.8 cm.
ii) Insulating layer of XPLE of thickness 2.3 cm and relative permittivity k = 2.2.
iii) Conducting lead sheath of thickness 2.9 mm.
iv) Insulating HDPE layer of thickness 5 mm and k = 2.4.
v) Outer coating negligible thickness in contact with soil.

My attempt:

I found the XPLE to have a capacitance of 310.70x10^-12 F/m.

To find the potential I assumed the charge between both conductors would equal 0, thus the charge on the inner conductor = -'ve charge on sheath. Hence I can use Q = CV to find the charge:

$$310.73x10^{-12} * \frac{220}{\sqrt{3}} = 3.95x10^{-5} C$$

Then to find potential between the two I use:

$$v = \frac{-Q}{2\pi\epsilon_0\epsilon_r}.ln(b/a)$$

$$\Rightarrow v = \frac{-Q}{2\pi * 8.8x10^{-12} * 2.4}.ln(0.0789/0.0739) = -19.5 kV$$

Which implies the potential on the lead sheath = $$\frac{220}{\sqrt{3}} kV + -19.5kV = 107.5kV$$

Have I done this right?

2. Jan 4, 2015

Staff: Admin

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

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